Search

In this study, we determine a new type comprehensive frame, which is called the generalized Frenet‐type frame in three‐dimensional Lie groups with Myller configurations, and it includes several special and classical type frames for Euclidean 3‐space and three‐dimensional Lie groups. After constructing this new comprehensive frame, we obtain derivative formulas with the help of the Lie curvature. In addition, we define some special type curves. The geometry of versor fields along a curve with Frenet‐type frame in three‐dimensional Lie groups with Myller configurations is a generalization of the usual theory of curves. Since this particular relationship, the osculating‐type and rectifying‐type curves with Frenet‐type frame in three‐dimensional Lie groups with Myller configurations include some special cases for osculating and rectifying curves in different spaces. [ABSTRACT FROM AUTHOR]

In this paper, the well‐posedness of Cauchy's problem of fractional Schrödinger equations with a power‐type nonlinearity on n‐dimensional manifolds with nonnegative Ricci curvature is studied. Under suitable volume conditions, the local solution with initial data in H[n2]+1 will blow up in finite time no matter how small the initial data is, which follows from a new weight function and ODE inequalities. Moreover, the upper‐bound of the lifespan can be estimated. [ABSTRACT FROM AUTHOR]

In this paper, we present a description of invariant twisted Kähler–Einstein (tKE) metrics on flag varieties. Additionally, we delve into the applications of the concepts utilized in proving our main result, particularly concerning the existence of the invariant twisted constant scalar curvature Kähler metrics. Moreover, we provide a precise description of the greatest Ricci lower bound for arbitrary Kähler classes on flag varieties. From this description, we establish a sequence of inequalities linked to optimal upper bounds for the volume of Kähler metrics, relying solely on tools derived from the Lie theory. Further, we illustrate our main results through various examples, encompassing full flag varieties, the projectivization of the tangent bundle of Pn+1${\mathbb {P}}^{n+1}$, and families of flag varieties with a Picard number 2. [ABSTRACT FROM AUTHOR]

Aim Methodology Results Conclusions To evaluate the agreement between six currently available periapical radiography‐based methods for measuring the root canal curvatures in mesial roots of mandibular first molars, assessed by two examiners with different proficiency levels.Non‐endodontically treated mesial roots of 41 human mandibular first molars were radiographed using the parallelling technique. Two independent observers (a specialist in endodontics and radiology and a final‐year dental student) assessed their root canal curvature using the methodologies described by Schneider (1971, Oral Surgery, Oral Medicine, Oral Pathology and Oral Radiology, 32, 271), Weine (1982, Endodontic therapy), Berbert and Nishiyama (1994, Revista Gaúcha de Odontología, 356), Luiten et al. (1995, Journal of Endodontics, 21, 26), Hankins and ElDeeb (1996, Journal of Endodontics, 22, 123) and Pettiette et al. (1999, Journal of Endodontics, 25, 230). Intra‐ and inter‐examiner reliability was assessed using the intraclass correlation coefficient. The differences in curvature angle measured by the different methods were compared using the one‐way anova for repeated measures test, followed by Tukey's post hoc analysis. The effect was calculated using the Cohen's d method. To determine the agreement between methods, the Bland–Altman analysis was used. The significance level was set at 5%.Agreement for the observers was excellent (>0.81) for the six methods considered. For the angle comparisons between methods, the maximum differences were for Schneider versus Weine (35.77°) and Luiten versus Hankins (35.14°), whilst the highest percentage of angles with a difference >10° were Weine versus Luiten and Berbert versus Pettiette (90%) and the comparison Weine versus Hankins presented with the lowest frequency (15%). Excellent agreement was found for five comparisons: Weine versus Luiten (0.940), Berbert versus Pettiette (0.917), Weine versus Pettiette (0.907), Luiten versus Pettiette (0.904) and Berbert versus Luiten (0.812). Compared to Schneider's method, the other methods showed a tendency of increasing difference as the angles became more acute. The other methods exhibited linear differences, remaining constant for smaller and larger angles.Reliability was excellent for all methods assessed separately. Maximum differences in curvature angles were found when comparing Schneider versus Weine and Luiten versus Hankins. Excellent agreement was found for Weine versus Luiten, Berbert versus Pettiette, Weine versus Pettiette, Luiten versus Pettiette and Berbert versus Luiten. In the presence of dilacerations, the method by Schneider was less sensitive. [ABSTRACT FROM AUTHOR]

We consider the class S⊥m(Ω)${\bf S}^m_\perp (\Omega)$ of m$m$‐dimensional surfaces in Ω¯⊂Rn$\overline{\Omega } \subset {\mathbb {R}}^n$ that intersect S=∂Ω$S = \partial \Omega$ orthogonally along the boundary. A piece of an affine m$m$‐plane in S⊥m(Ω)${\bf S}^m_\perp (\Omega)$ is called an orthogonal slice. We prove estimates for the area by the Lp$L^p$ integral of the second fundamental form in three cases: first, when Ω$\Omega$ admits no orthogonal slices, second for m=p=2$m = p = 2$ if all orthogonal slices are topological disks, and finally, for all Ω$\Omega$ if the surfaces are confined to a neighborhood of S$S$. The orthogonality constraint has a weak formulation for curvature varifolds. We classify those varifolds of vanishing curvature. As an application, we prove for any Ω$\Omega$ the existence of an orthogonal 2‐varifold that minimizes the L2$L^2$ curvature in the integer rectifiable class. [ABSTRACT FROM AUTHOR]

Purpose: Autostereoscopic displays have become increasingly common, but their impact on ocular dimensions remains unknown. We sought to identify changes in the crystalline lens dimensions induced by autostereoscopic three‐dimensional (3D) viewing. Methods: Forty young adults (age: 22.6 ± 2.0 years, male/female: 15/25) were consecutively enrolled and randomly divided into two groups (3D and two‐dimensional [2D] viewing groups) to watch a 30‐min movie clip displayed in 3D or 2D mode on a tablet computer. The lens thickness (LT), diameter, curvature, decentration and tilt were measured with anterior segment optical coherence tomography under both non‐accommodating (static) and accommodating conditions. Results: In the static condition, the LT decreased by 0.03 ± 0.03 mm (p < 0.001) and the anterior radius of curvature (ARC) increased by 0.49 ± 0.59 mm (p = 0.001) post‐3D viewing. In contrast, following 2D viewing, the ARC decreased by 0.23 ± 0.25 mm (p = 0.001). Additionally, the increase in the steep ARC post‐3D viewing was greater in high‐myopic eyes than low to moderate myopic eyes (p = 0.04). When comparing the accommodative with the static (non‐accommodative) condition, for 3D viewing the lens decentration decreased (−0.03 ± 0.05 mm, p = 0.02); while for 2D viewing, the posterior curvature radius (−0.14 ± 0.20 mm, p = 0.006) and diameter (−0.13 ± 0.20 mm, p = 0.01) decreased. Conclusions: Viewing with the autostereoscopic 3D tablet could temporally decrease the thickness and curvature of the lens under non‐accommodating conditions. However, its long‐term effect requires further exploration. [ABSTRACT FROM AUTHOR]

We propose a notion of stability for constant k$k$‐mean curvature hypersurfaces in a general Riemannian manifold and we give some applications. When the ambient manifold is a Space Form, our notion coincides with the known one, given by means of the variational problem. [ABSTRACT FROM AUTHOR]

Let d≥3$d\ge 3$ be an integer. For a holomorphic d$d$‐web W$\mathcal {W}$ on a complex surface M$M$, smooth along an irreducible component D$D$ of its discriminant Δ(W)$\Delta (\mathcal {W})$, we establish an effective criterion for the holomorphy of the curvature of W$\mathcal {W}$ along D$D$, generalizing results on decomposable webs due to Marín, Pereira, and Pirio. As an application, we deduce a complete characterization for the holomorphy of the curvature of the Legendre transform (dual web) LegH$\mathrm{Leg}\mathcal {H}$ of a homogeneous foliation H$\mathcal {H}$ of degree d$d$ on PC2$\mathbb {P}^{2}_{\mathbb {C}}$, generalizing some of our previous results. This then allows us to study the flatness of the d$d$‐web LegH$\mathrm{Leg}\mathcal {H}$ in the particular case where the foliation H$\mathcal {H}$ is Galois. When the Galois group of H$\mathcal {H}$ is cyclic, we show that LegH$\mathrm{Leg}\mathcal {H}$ is flat if and only if H$\mathcal {H}$ is given, up to linear conjugation, by one of the two 1‐forms ω1d=yddx−xddy$\omega _1^{d}=y^d\mathrm{d}x-x^d\mathrm{d}y$, ω2d=xddx−yddy$\omega _2^{d}=x^d\mathrm{d}x-y^d\mathrm{d}y$. When the Galois group of H$\mathcal {H}$ is noncyclic, we obtain that LegH$\mathrm{Leg}\mathcal {H}$ is always flat. [ABSTRACT FROM AUTHOR]

Laboratory experiments and numerical simulations were performed to explore the influence of intersection geometry on fluid flow and solute transport in fractures. Fractures were engraved and sealed into an acrylic plate and two orthogonal intersections with different geometry were constructed. The effects of curvature and relative shear displacement at intersections on preferential flow and solute transport were investigated. By solving the Navier–Stokes (NS) equation, the fluid mixing and solute distribution were predicted. The results showed that the geometric characteristics at the intersection have a significant effect on the preferential flow and solute distribution. The results agreed well with the experimental results, in terms of flow direction, preferential flow rate, and heterogeneous solute distribution. With an increase in curvature, the flow difference between the two outlets increases gradually. Increasing curvature can reduce the preferential flow and weaken the inhomogeneity of solute distribution. An increase of relative shear displacement decreases the pressure gradient and flow rate at the entrance of the two branch fractures, and thereby increases preferential flow and inhomogeneity of solute distribution. The results provide a basis and reference for further exploring the relationship between the geometric characteristics of fracture intersections and flow behaviors. [ABSTRACT FROM AUTHOR]

The renewed focus on eye growth in preterm‐born children was primarily triggered by Danish cohort studies, including the Copenhagen Project, which focused on children born from 1959–1961. The retinotoxic effects of excessive oxygen on premature neonates had long been clarified and therapeutically adjusted for. Later, ultrasound oculometry and keratometry established that ocular size deficits, linked to development, also occurred in normally developing children, not just frail outliers. This indicated that general catch‐up had not been achieved. This paper discusses whether one early segment of eye development does not occur in preterm, and here even in more robust neonates, without later compensation. [ABSTRACT FROM AUTHOR]

A directionally‐split volume‐of‐fluid (VOF) methodology for evolving interfaces under curvature‐dependent speed is devised. The interface is reconstructed geometrically and the volume fraction is advected with a technique to incorporate a topological volume conservation constraint. The proposed approach uses the idea that the role of curvature in a speed function V$$ \mathbf{V} $$ is analogous to the role of viscosity in the corresponding hyperbolic conservation law to propagate complex interfaces where singularities may exist. The approach has the advantage of simple implementation and straightforward extension to more complex multiphase systems by formulating the interface evolution problem using energy functionals to derive an expression for the interface‐advecting velocity. The numerical details of the volume‐of‐fluid based formulation are discussed with emphasis on the importance of curvature estimation. Finally, canonical curves and surfaces traditionally investigated by the level set (LS) method are tested with the devised approach and the results are compared with existing work in LS. [ABSTRACT FROM AUTHOR]

Heusler compounds belong to a large family of materials and exhibit numerous physical phenomena with promising applications, particularly ferromagnetic Weyl semimetals for their use in spintronics and memory devices. Here, anomalous Hall transport is reported in the room‐temperature ferromagnets NiMnSb (half‐metal with a Curie temperature (TC) of 660 K) and PtMnSb (pseudo half‐metal with a TC of 560 K). They exhibit 4 µB/f.u. magnetic moments and non‐trivial topological states. Moreover, NiMnSb and PtMnSb are the first half‐Heusler ferromagnets to be reported as Weyl semimetals, and they exhibit anomalous Hall conductivity (AHC) due to the extended tail of the Berry curvature in these systems. The experimentally measured AHC values at 2 K are 1.8 × 102 Ω−1 cm−1 for NiMnSb and 2.2 × 103 Ω−1 cm−1 for PtMnSb. The comparatively large value between them can be explained in terms of the spin‐orbit coupling strength. The combined approach of using ab initio calculations and a simple model shows that the Weyl nodes located far from the Fermi energy act as the driving mechanism for the intrinsic AHC. This contribution of topological features at higher energies can be generalized. [ABSTRACT FROM AUTHOR]

Highlights Application of the global Gauss–Bonnet theorem for the prediction of changes in Gaussian curvature for double curvature laminate geometries due to shrinkage is developed for non‐isometric deformation states where in surface area change accompanies changes in curvature. The transition between isometric and non‐isometric deformation is strongly influenced by the ratio of the principal radii of curvature of the double curved surface and a relationship is proposed by the authors to accommodate the transition. Examples for the radii of curvature ratios of 2, 3, and 4 are compared to results from finite‐element simulations and the developed relationship is shown to be accurate within 0.55%. Furthermore, these results demonstrate that isometric deformation state can be taken as an adequate representation for double curvature toroidal laminate geometries of ρ2/ρ1$$ {\rho}_2/{\rho}_1 $$ >10 and the class of materials studied in this work. Shrinkage induced deformation in multi‐curvature composite laminates is a recurring issue in polymer composite manufacturing. Thermal, crystallization and cure shrinkage are the dominant sources of shrinkage deformation in polymer composite systems. Isometric deformation of multi‐curvature, symmetric laminates composite is defined by the absence of membrane strain. The Gauss–Bonnet theorem provides a platform for determining radii of curvature changes in multi‐curvature symmetric laminates, Non‐isometric deformation of symmetric laminates can be treated by the Gauss–Bonnet theorem for radii of curvature ratios that correspond to geometric self‐constraint. The above highlights yield insight into the anticipated geometric distortions due to shrinkage in polymer composites. [ABSTRACT FROM AUTHOR]

Translation abstract A mechanically consistent approach for stability verification of timber beams in compression and bending around the strong axis – part 2: experimental tests and numerical simulationSlender timber beams in bending can be designed using different methods in view of out‐of‐plane stability. Lateral torsional buckling may be verified either using the so called equivalent member method or by means of 2nd order calculations, considering equivalent imperfections. Applying current codes, however, determining the lateral torsional buckling resistance using either of these both methods, leads to different results. In this paper, the background of both verifications is investigated in deep. Moreover, as an alternative approach, a non‐linear calculation with an imperfection shape in affinity to the critical shape was presented in part 1 of this paper. By scaling the curvature, the same results as by the equivalent member method can be achieved. It was shown that plasticity effects can be considered as well. In this part 2, results of lateral torsional buckling tests on glued laminated timber beams are presented, with nearly ideal boundary conditions and load direction remaining vertical through‐out the test. Based on these test first tentative values can be obtained for the imperfection compatible with the alternative lateral torsional buckling approach presented. [ABSTRACT FROM AUTHOR]

We compute a lower bound for the scalar curvature of a gradient Einstein soliton under a certain assumption on its potential function. We establish an asymptotic behavior of the potential function on a noncompact gradient shrinking Einstein soliton. As a result, we obtain the finiteness of its fundamental group and its weighted volume. We also prove some geometric and analytic results for constructing gradient Einstein solitons that are realized as warped metrics, and we give a few explicit examples. [ABSTRACT FROM AUTHOR]

This study aimed to determine the parameter priority for the design optimization of circular concrete‐filled double skin tubular (CFDST) slender beam‐columns under eccentric loading. Experimental investigations were conducted on four geometrically distinct CFDST beam‐columns subjected to eccentric loading to analyze their behavioral responses. A finite element (FE) model was developed and calibrated using the experimental data. The FE simulations were performed on seven parameters, including load eccentricity, concrete strength, steel strength, outer tube thickness, inner tube thickness, lateral curvature, and end fixity to determine their respective impacts. By varying each parameter by 10%, the ultimate capacity of the columns was affected by different percentages. The load eccentricity was found to have the highest contribution of 58.7%, followed by fixity (16.0%), steel strength (9.3%), outer tube thickness (8.8%), inner tube thickness (3.5%), concrete strength (2.5%), and lateral curvature (1.2%). These findings establish the priority of the parameters, highlighting the significance of load eccentricity in the optimization of circular CFDST slender beam‐columns under eccentric loading. [ABSTRACT FROM AUTHOR]

Exploring the four‐dimensional AdS black hole is crucial within the framework of the AdS/CFT correspondence. In this research, four‐dimensional stationary and rotating AdS solutions in the framework of the f(Q)$f(Q)$ gravitational theory are investigated, considering the charged scenario. Author's emphasis is on the power‐law ansatz, which consistent with observations and is deemed the most viable. Because this solution does not have an uncharged version or relate to general relativity, it falls into a new category, which derives its features from changes in non‐metricity and incorporates the Maxwell domain. The singularities of such a solution are analyzed, computing all the quantities of different curvature and non‐metricity invariants. Author's results indicate the presence of a central singularity, albeit with a softer nature compared to standard non‐metricity or Einstein general relativity, attributed to the influence of the effect of f(Q)$f(Q)$. Several physical characteristics of black hole from thermodynamics perspective and demonstrate the existence of an outer event horizon in addition to the inner Cauchy horizons are examined. However, under the conditions of sufficiently large electric charge, a naked singularity emerges. Finally, a class of rotating black hole in four‐dimensional f(Q)$f(Q)$ gravity that are asymptotically anti‐de Sitter charged is derived. Exploring the four‐dimensional AdS black hole is crucial within the framework of the AdS/CFT correspondence. In this research, four‐dimensional stationary and rotating AdS solutions in the framework of the f(Q)$f(Q)$ gravitational theory are investigated, considering the charged scenario. Author's emphasis is on the power‐law ansatz, which consistent with observations and is deemed the most viable. Because this solution does not have an uncharged version or relate to general relativity, it falls into a new category, which derives its features from changes in non‐metricity and incorporates the Maxwell domain. The singularities of such a solution are analyzed, computing all the quantities of different curvature and non‐metricity invariants. Author's results indicate the presence of a central singularity, albeit with a softer nature compared to standard non‐metricity or Einstein general relativity, attributed to the influence of the effect of f(Q)$f(Q)$ Several physical characteristics of black hole from thermodynamics perspective and demonstrate the existence of an outer event horizon in addition to the inner Cauchy horizons are examined. However, under the conditions of sufficiently large electric charge, a naked singularity emerges. Finally, a class of rotating black hole in four‐dimensional f(Q)$f(Q)$ gravity that are asymptotically anti‐de Sitter charged is derived. [ABSTRACT FROM AUTHOR]

Screen printing is an interesting technique for the high‐volume production of printed conductive electronic devices on flexible substrates. In this study, silver conductive lines have been produced by screen‐printing technique on flexible PEN substrates and optimized in order to provide maximum electrical conduction. The geometry of the obtained conductive samples has been modified by performing thermoforming tests in a mold with complex geometry, replicating a significant section of dashboard coating. The functionality of the shape‐deformed substrates has been assessed. [ABSTRACT FROM AUTHOR]

Wearable technology excels in estimating kinematic and physiological data, but estimating biological torques remains an open challenge. Deformation of the skin above contracting muscles—surface‐level muscle deformation—has emerged as a promising signal for joint torque estimation. However, a lack of ground‐truth measures of surface‐level muscle deformation has complicated the evaluation of wearable sensors designed to measure surface‐level muscle deformation. A non‐contact methodology is proposed for ground‐truth measurement of surface‐level muscle deformation using a 2D laser profilometer. It shows how three metrics of surface‐level muscle deformation—peak radial displacement: r = 0.94 ± 0.05, surface curvature: r= 0.78 ± 0.10, surface strain: r = 0.83 ± 0.12—correlate strongly to changes in volitional elbow torque, further exploring the impact of measurement location or joint angle on these relationships. A nonlinear, lead‐lag relationship between surface‐level muscle deformation and torque is also found. The findings suggest that surface‐level muscle deformation is a promising signal for non‐invasive, real‐time estimates of torque. By standardizing measurement, the methodology can help inform the design of future wearable sensors. [ABSTRACT FROM AUTHOR]

We introduce several new notions of (sectional) curvature bounds for Lorentzian pre‐length spaces: On the one hand, we provide convexity/concavity conditions for the (modified) time separation function, and, on the other hand, we study four‐point conditions, which are suitable also for the non‐intrinsic setting. Via these concepts, we are able to establish (under mild assumptions) the equivalence of all previously known formulations of curvature bounds. In particular, we obtain the equivalence of causal and timelike curvature bounds as introduced by Kunzinger and Sämann. [ABSTRACT FROM AUTHOR]

In this paper, we prove the following geometric inequalities in the Euclidean space Rn(n⩾3)$\mathbb {R}^n \ (n\geqslant 3)$, which are weighted Alexandrov–Fenchel type inequalities, ∫Σr2αHkdμ⩾ωn−1∫ΣHldμωn−1n−1−k+2αn−1−l,for0⩽l

Diameter estimates for Kähler metrics are established which require only an entropy bound and no lower bound on the Ricci curvature. The proof builds on recent PDE techniques for L∞$L^\infty$ estimates for the Monge–Ampère equation, with a key improvement allowing degeneracies of the volume form of codimension strictly greater than one. As a consequence, we solve the long‐standing problem of uniform diameter bounds and Gromov–Hausdorff convergence of the Kähler–Ricci flow, for both finite‐time and long‐time solutions. [ABSTRACT FROM AUTHOR]

Energetic electron precipitation (EEP) during substorms significantly affects ionospheric chemistry and lower‐ionosphere (<100 km) conductance. Two mechanisms have been proposed to explain what causes EEP: whistler‐mode wave scattering, which dominates at low latitudes (mapping to the inner magnetosphere), and magnetic field‐line curvature scattering, which dominates poleward. In this case study, we analyzed a substorm event demonstrating the dominance of curvature scattering. Using ELFIN, POES, and THEMIS observations, we show that 50–1,000 keV EEP was driven by curvature scattering, initiated by an intensification and subsequent earthward motion of the magnetotail current sheet. Using a combination of Swarm, total electron content, and ELFIN measurements, we directly show the location of EEP with energies up to ∼1 MeV, which extended from the plasmapause to the near‐Earth plasma sheet (PS). The impact of this strong substorm EEP on ionospheric ionization is also estimated and compared with precipitation of PS (<30 keV) electrons. Plain Language Summary: During magnetospheric substorms, energetic electrons in the Earth's plasma sheet (PS), the night‐side magnetosphere region filled by hot plasma, precipitate to the ionosphere. Energetic electron precipitation (EEP) affects the density, temperature, and composition of the ionosphere. However, the exact process that causes such precipitation is not well understood due to observational constraints. The challenge lies in simultaneously measuring the EEP properties at the ionosphere and the plasma and wave properties in the PS. We analyze a fortuitous satellite conjunction during a substorm, during which EEP was simultaneously captured by ELFIN, Swarm, and POES at low altitudes, and THEMIS in the equatorial PS. EEP was observed to extend across a broad equatorial domain, projecting into a wide ionospheric region and encompassing the PS region and a significant portion of the inner magnetosphere. High‐energy‐resolution measurements from ELFIN reveal that the main driver of precipitation is the scattering of energetic electrons by strongly curved magnetic field lines in the PS, as opposed to the more commonly suggested scattering mechanisms associated with wave‐particle interactions. We also show that the EEP drastically altered the ionization profile of the ionosphere. Key Points: We investigate the radial location of energetic (50–1,000 keV) electron precipitation (EEP) during a substormWe compare the impact of plasma sheet electron precipitation (<30 keV) and EEP (50–1,000 keV) on the altitudinal profile of ionizationOur results underscore the key role of curvature scattering in energetic electron precipitation during substorms [ABSTRACT FROM AUTHOR]

In this paper, the motion of strictly convex closed plane curves under dissipative hyperbolic mean curvature flow is studied. The hyperbolic Monge–Amp è$$ \overset{\grave }{e} $$re equation is derived by using the support function. The short‐time existence of the flow is proved, and some evolution equations are derived. Furthermore, according to different initial velocities, we discuss the expansion and contraction of the dissipative hyperbolic curvature flow; that is, if the initial velocity v˜0<−α2ω0(θ)$$ {\tilde{v}}_0<-\frac{\alpha }{2}{\omega}_0\left(\theta \right) $$, the flow will converge to the limit curve at a finite time; if the initial velocity v˜0=−α2ω0(θ)$$ {\tilde{v}}_0&#x0003D;-\frac{\alpha }{2}{\omega}_0\left(\theta \right) $$, the flow will converge to a point t→∞$$ t\to \infty $$; if the initial velocity −−α2ω0(θ)0$$ {\tilde{v}}_0\left(\theta \right)>0 $$, the flow will expand to a limit curve as t→∞$$ t\to \infty $$. [ABSTRACT FROM AUTHOR]

Previous studies have reported sex differences in cortical gyrification. Since most cortical folding is principally defined in utero, sex chromosomes as well as gonadal hormones are likely to influence sex‐specific aspects of local gyrification. Classic congenital adrenal hyperplasia (CAH) causes high levels of androgens during gestation in females, whereas levels in males are largely within the typical male range. Therefore, CAH provides an opportunity to study the possible effects of prenatal androgens on cortical gyrification. Here, we examined the vertex‐wise absolute mean curvature—a common estimate for cortical gyrification—in individuals with CAH (33 women and 20 men) and pair‐wise matched controls (33 women and 20 men). There was no significant main effect of CAH and no significant CAH‐by‐sex interaction. However, there was a significant main effect of sex in five cortical regions, where gyrification was increased in women compared to men. These regions were located on the lateral surface of the brain, specifically left middle frontal (rostral and caudal), right inferior frontal, left inferior parietal, and right occipital. There was no cortical region where gyrification was increased in men compared to women. Our findings do not only confirm prior reports of increased cortical gyrification in female brains but also suggest that cortical gyrification is not significantly affected by prenatal androgen exposure. Instead, cortical gyrification might be determined by sex chromosomes either directly or indirectly—the latter potentially by affecting the underlying architecture of the cortex or the size of the intracranial cavity, which is smaller in women. [ABSTRACT FROM AUTHOR]

The unique morphology of 2D van der Waals materials enables them to withstand large deformations and significant nonuniform strain, potentially inducing a strong flexoelectric effect. Despite the size‐dependent flexoelectric effect showing potential for modulating the optoelectronic performance of 2D van der Waals materials, it is far from being fully exploited owing to various challenges. Herein, the use of nanowires with different diameters as the bending media to fabricate 2D α‐In2Se3/β‐InSe heterojunctions with large curvatures of 0.1–1 µm−1 is proposed. The significant band alignment modulation in α‐In2Se3 resulting from the bending‐induced flexoelectric effect is verified through Kelvin probe force microscopy. The strain‐induced piezoelectric effect can be negated because of the weak vdW forces at the interface. The flexoelectric polarization in β‐InSe is screened via the accumulated electrons in the unilateral depleted heterojunction. Compared to the flat heterojunction, the curved heterojunction with an average curvature of 0.9 µm−1 shows 2.48‐fold and 7.62‐fold increases in open‐circuit voltage and zero‐biased responsivity, respectively. This study demonstrates the first successful modulation of photodetection in 2D heterojunctions by exploiting the flexoelectric effect, providing a new perspective for high‐performance 2D vdW optoelectronic devices. [ABSTRACT FROM AUTHOR]

A theorem of Llarull says that if a smooth metric g$g$ on the n$n$‐sphere Sn$\mathbb {S}^n$ is bounded below by the standard round metric and the scalar curvature Rg$R_g$ of g$g$ is bounded below by n(n−1)$n (n - 1)$, then the metric g$g$ must be the standard round metric. We prove a spectral Llarull theorem by replacing the bound Rg⩾n(n−1)$R_g \geqslant n (n - 1)$ by a lower bound on the first eigenvalue of an elliptic operator involving the Laplacian and the scalar curvature Rg$R_g$. We utilize two methods: spinor and spacetime harmonic function. [ABSTRACT FROM AUTHOR]

The existence of bound states for the magnetic Laplacian in unbounded domains can be quite challenging in the case of a homogeneous magnetic field. We provide an affirmative answer for almost flat corners and slightly curved half‐planes when the total curvature of the boundary is positive. [ABSTRACT FROM AUTHOR]

In this paper, inspired by Brendle (Comm. Pure Appl. Math. 76 (2023), 2192) and Johne (arXiv:2103.08496, 2021), we prove a Sobolev inequality on manifolds with density and asymptotically nonnegative Bakry–Émery Ricci curvature. [ABSTRACT FROM AUTHOR]

We prove the existence of nontrivial closed surfaces with constant anisotropic mean curvature with respect to elliptic integrands in closed smooth 3$\hskip.001pt 3$–dimensional Riemannian manifolds. The constructed min‐max surfaces are smooth with at most one singular point. The constant anisotropic mean curvature can be fixed to be any real number. In particular, we partially solve a conjecture of Allard in dimension 3$\hskip.001pt 3$. [ABSTRACT FROM AUTHOR]

Summary: The use of curved forms in tall buildings has increased recently due to their structural and esthetic advantages. Diagrid structures are typically used for these buildings because of their ability to express curved forms. There are, however, few studies about the curvature of tall buildings. This paper examines the effect of curvature on the wind force on tall curved buildings with diagrid system. So, to achieve this, the form of tall curved buildings is investigated, and the commonly used equations that constitute their form are determined. Then, applying computational fluid dynamics simulation, wind force was calculated on the developed alternatives which were created by the equations. Besides, the structural mass of each model is calculated by optimizing the cross‐section of the members. It is concluded that considering the conditions of the applied model, by increasing the concavity of the form, the suction on the building's facade increases. Further, with the increase of the concavity in the plan and elevation, the along wind force on the structure and overturning moment increases. Also, it is observed that the structural efficiency of curvilinear buildings is only appropriate to a certain extent of curvature, and with its increase, the structural efficiency decreases. This article offers useful information for the preliminary design of tall buildings. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive study of the intrinsic strain response of 3D heterostructures arising from lattice mismatch. Combining materials with different lattice constants induces strain, leading to the bending of these heterostructures. We propose a model for nonlinear elastic heterostructures such as bimetallic beams or nanowires that takes into account local prestrain within each distinct material region. The resulting system of partial differential equations (PDEs) in Lagrangian coordinates incorporates a nonlinear strain and a linear stress‐strain relationship governed by Hooke's law. To validate our model, we apply it to bimetallic beams and hexagonal hetero‐nanowires and perform numerical simulations using finite element methods (FEM). Our simulations examine how these structures undergo bending under varying material compositions and cross‐sectional geometries. In order to assess the fidelity of the model and the accuracy of simulations, we compare the calculated curvature with analytically derived formulations. We derive these analytical expressions through an energy‐based approach as well as a kinetic framework, adeptly accounting for the lattice constant mismatch present at each compound material of the heterostructures. The outcomes of our study yield valuable insights into the behavior of strained bent heterostructures. This is particularly significant as the strain has the potential to influence the electronic band structure, piezoelectricity, and the dynamics of charge carriers. [ABSTRACT FROM AUTHOR]

Contactless hot embossing has been demonstrated to possess the potential for cost‐effective production and precise mounting concepts in fabricating glass microlenses and microlens arrays due to the reduced difficulty of mold fabrication and the possibility of obtaining self‐aligned assemblies. This study aims to provide experimental evidence for understanding the forming mechanism of glass microlenses and microlens arrays in the contactless hot embossing process. The effects of process parameters, diameter and position of the micro‐holes, hole diameter, and pitch of the micro‐hole array mold on the filling deformation of glass in contactless hot embossing were comprehensively investigated. It is found that placing the micro‐hole farther away from the mold center renders decrease in both filling height and tip curvature but increase in the eccentricity of the embossed glass microlens. As a result, the formed glass microlens array shows a nonuniform distribution of filling height and tip curvature. Furthermore, reducing the pitch of micro‐hole array mold can significantly improve the uniformity of formed microlens array. Based on these experimental results, the forming mechanism of microlenses and microlens arrays in contactless hot embossing process is summarized. Finally, a glass microlens array with decent uniformity in the center area was hot embossed by using a SiC micro‐hole array mold. [ABSTRACT FROM AUTHOR]

A notable example due to Heier, Lu, Wong, and Zheng shows that there exist compact complex Kähler manifolds with ample canonical line bundle such that the holomorphic sectional curvature is negative semi‐definite and vanishes along high‐dimensional linear subspaces in every tangent space. The main result of this note is an upper bound for the dimensions of these subspaces. Due to the holomorphic sectional curvature being a real‐valued bihomogeneous polynomial of bidegree (2,2) on every tangent space, the proof is based on making a connection with the work of D'Angelo on complex subvarieties of real algebraic varieties and the decomposition of polynomials into differences of squares. Our bound involves an invariant that we call the holomorphic sectional curvature square decomposition length, and our arguments work as long as the holomorphic sectional curvature is semi‐definite, be it negative or positive. [ABSTRACT FROM AUTHOR]

Solubility enhancement is a key issue for developing the perylene diimide‐based functional materials. Introduction of curved structure proved an effective solubilizing method without employing steric repulsion. In this work, wavily curved perylene diimides were developed as a new family of highly soluble curved perylene diimides. Moreover, their conformational dynamics, aggregating properties, electronic properties, and photovoltaic performances were thoroughly examined in comparison to the previously reported isomer exhibiting an arched curvature. The waved isomer demonstrated heightened rigidity and a greater propensity for aggregation compared to the arched isomer, likely attributed to its more planar structure. Each benzoxepin unit played a role in cancelling out the curvature on the opposite side. While the difference in the molecular curvature did not cause significant alterations in the photophysical and electron‐accepting properties, we identified that the modulation of the curved structure is effective in controlling the morphology of the photoelectric conversion layer. [ABSTRACT FROM AUTHOR]

The study of the minimality of (hyper)surfaces is a fundamental problem in mathematics with major applications in both fundamental and applied sciences. Recently, the minimality of production models in microeconomics has been investigated by several authors who obtained important classification results for quasi‐sum and quasi‐product production functions with two and three inputs. In the present work, we deal with the minimality of isoquants of production functions with arbitrary number of inputs, this being a key concept used in making the best decision for optimizing the production costs. In the main result of the article, we give the complete classification of quasi‐product production functions whose isoquants are minimal, showing that there are exactly nine production models with such a property. Among them, we can identify a particular classic model already widely used in economic analysis (viz., a Cobb–Douglas model with unit output elasticities with respect to some production factors) and various production models completely unknown until now and which will open new opportunities for applied research in the field of mathematical economics. [ABSTRACT FROM AUTHOR]

While (2+1)$(2+1)$‐dimensional black holes in the Einstein theory allow for only the anti‐de Sitter (AdS) asymptotic, when the higher curvature correction is tuned on, the asymptotically flat, de Sitter, and AdS cases are included. Here, a detailed study of the stability and quasinormal spectra of the scalar field perturbations around such black holes with all three asymptotics is proposed. Calculations of the frequencies are fulfilled with the help of the 6th order Wentzel–Kramers–Brillouin (WKB) method with Pade approximants, Bernstein polynomial method, and time‐domain integration. Results obtained by all three methods are in a very good agreement in their common range of applicability. When the multipole moment k$k$ is equal to zero, the purely imaginary, i.e., non‐oscillatory, modes dominate in the spectrum for all types of the asymptotic behavior, while the spectrum at higher k$k$ resembles that in four‐dimensional spacetime with the corresponding asymptotic. While (2 + 1)‐dimensional black holes in the Einstein theory allow for only the anti‐de Sitter (AdS) asymptotic, when the higher curvature correction is tuned on, the asymptotically flat, de Sitter, and AdS cases are included. Here, a detailed study of the stability and quasinormal spectra of the scalar field perturbations around such black holes with all three asymptotics is proposed. Calculations of the frequencies are fulfilled with the help of the 6th order Wentzel–Kramers–Brillouin (WKB) method with Pade approximants, Bernstein polynomial method, and time‐domain integration. Results obtained by all three methods are in a very good agreement in their common range of applicability. When the multipole moment k is equal to zero, the purely imaginary, i.e., non‐oscillatory, modes dominate in the spectrum for all types of the asymptotic behavior, while the spectrum at higher k resembles that in four‐dimensional spacetime with the corresponding asymptotic. [ABSTRACT FROM AUTHOR]

Remnant fabrics inherited from mid‐ridge play a key role in variations of plate deformation, hydration and seismicity along subduction zones. However, the quantitative relationships between the orientation of these remnant faults, plate bending and seismic activity at subduction zones still remain unclear. Here, we investigated the flexure of the Alaska subducting plate and assessed the relations between plate flexural curvatures, trench–fabric angle and seismicity. The results show that the flexural curvature and seismicity have nearly linear relationships with the trench–fabric angle. We find that remnant faults are more likely to be reactivated by plate bending at low trench–fabric angle region, causing greater plate deformation, hydration, weakening and seismicity. Plate weakening in turn promotes flexural bending curvature, resulting in higher degree of fracture and more earthquakes. However, at the high trench–fabric angle region, it is inclined to form new trench‐parallel bending faults that have smaller bending curvature and less seismicity. [ABSTRACT FROM AUTHOR]

The flexible printed OLED TV display technology will be able to create new application market, such as rollable/foldable TV, in the future. It's TV Mobiles. Since the TCL (TCL CSOT, Guangdong Juhua Printed Display Technology Co. Ltd. & TCL Corporate Research) has successfully demonstrated the 31" FHD flexible printed OLED TV, there are a lot of technology breakthroughs for improving the panel performance and cost reduction. The co‐planar top gate Oxide TFT device architecture, printing OLED top emission device architecture with new OLED materials, MURA free ink jet printing technology with unique bank design, advanced encapsulation technology with new inorganic material for panel performance improvement are developed. Especially innovative mechanical release technology without using laser lift off technology is developed for cost reduction and production yield up in flexible printed OLED TV MP line. Based on these technology breakthroughs, 31" 4K flexible printed OLED TV with high resolution(142ppi) are fabricated. The performance of 31" flexible printed OLED TV is, 4K high resolution (3840x2160, 142ppi), luminance: FW 150nits, excellent C/R; > 1M:1, color gamut: DCI‐P3: >99%, wide viewing angle (Δu'v' < 0.02): ≥ +/‐ 45°, A/R: 47.75%, and curvature radius: 20mm In this paper, the panel performance of 31" 4K high resolution flexible printed OLED TV and the latest technology breakthroughs are discussed in details. [ABSTRACT FROM AUTHOR]

Various near‐eye displays have been commercialized over the past decade. They are approaching to be a form of ordinary eyeglasses. The majority of researchers use planar waveguides as combiner, which do not distort the image beam while being transferred along the waveguide. However, planar combiners do not look like eyeglasses because they are flat, not curved. In this work an optical architecture with curved waveguide for near eye display is proposed. Two conditions for image transfer through curved waveguide are defined. These conditions have been satisfied using a compensator and grating with a law of variation of the grating period in the optical architecture. It was verified by prototyping to aim for eyeglasses with 150 mm radius of curvature of the curved waveguide with a thickness of 2 mm, which performs RGB full color, 30 degrees of field of view and 12×10 mm of eye box for all day use. [ABSTRACT FROM AUTHOR]

Magnetic field line curvature (FLC) scattering is an effective mechanism for collisionless particle scattering. In the terrestrial magnetosphere, the FLC scattering plays an essential role in shaping the outer boundary of protons radiation belt, the rapid decay of ring current, and the formation of proton isotropic boundary (IB). However, previous studies have yet to adequately investigate the influence of FLC scattering on charged particles in the Earth's dayside magnetosphere, particularly in the off‐equatorial magnetic minima regions. This study employs T89 magnetic field model to investigate the impacts of FLC scattering on ring current protons in the dayside magnetosphere, with a specific focus on the off‐equatorial minimum regions. We analyze the spatial distributions of single and dual magnetic minima regions, adiabatic parameter, and pitch angle diffusion coefficients due to FLC scattering as functions of Kp. The results show that the effects of FLC scattering are significant not only on the dusk and dawn sides but also in the off‐equatorial minima regions on the noon. Additionally, we investigate the role of dipole tilt angle in the hemispheric asymmetry of FLC scattering effects. The dipole tilt angle controls the overall displacement of the dayside magnetosphere, resulting in different FLC scattering effects in the two hemispheres. Our study holds significance for understanding the FLC scattering effects in the off‐equatorial region of Earth's dayside magnetosphere and for constructing a more accurate dynamic model of particles. Key Points: Ring current protons in the dayside off‐equatorial regions are significantly affected by field line curvature (FLC) scatteringThe scattering effects driven by FLC on protons display distinct hemispheric asymmetry in the dayside off‐equatorial regionsThe dipole tilt angle affects hemispheric asymmetry, thereby influencing the strength and extent of FLC scattering [ABSTRACT FROM AUTHOR]

Smooth and curved microstructural topologies found in nature—from soap films to trabecular bone—have inspired several mimetic design spaces for architected metamaterials and bio‐scaffolds. However, the design approaches so far are ad hoc, raising the challenge: how to systematically and efficiently inverse design such artificial microstructures with targeted topological features? Herein, surface curvature is explored as a design modality and a deep learning framework is presented to produce topologies with as‐desired curvature profiles. The inverse design framework can generalize to diverse topological features such as tubular, membranous, and particulate features. Moreover, successful generalization beyond both the design and data space is demonstrated by inverse designing topologies that mimic the curvature profile of trabecular bone, spinodoid topologies, and periodic nodal surfaces for application in bio‐scaffolds and implants. Lastly, curvature and mechanics are bridged by showing how topological curvature can be designed to promote mechanically beneficial stretching‐dominated deformation over bending‐dominated deformation. [ABSTRACT FROM AUTHOR]

Maintaining lipid asymmetry across membrane leaflets is critical for functions like vesicular traffic and organelle homeostasis. However, a lack of molecular‐level understanding of the mechanisms underlying membrane fission and fusion processes in synthetic systems precludes their development as artificial analogs. Here, we report asymmetry induction of a bilayer membrane formed by an extended π‐conjugated molecule with oxyalkylene side chains bearing terminal tertiary amine moieties (BA1) in water. Autogenous protonation of the tertiary amines in the periphery of the bilayer by water induces anisotropic curvature, resulting in membrane fission to form vesicles and can be monitored using time‐dependent spectroscopy and microscopy. Interestingly, upon loss of the induced asymmetry by extensive protonation using an organic acid restored bilayer membrane. The mechanism leading to the compositional asymmetry in the leaflet and curvature induction in the membrane is validated by density functional theory (DFT) calculations. Studies extended to control molecules having changes in hydrophilic (BA2) and hydrophobic (BA3) segments provide insight into the delicate nature of molecular scale interactions in the dynamic transformation of supramolecular structures. The synergic effect of hydrophobic interaction and the hydrated state of BA1 aggregates provide dynamicity and unusual stability. Our study unveils mechanistic insight into the dynamic transformation of bilayer membranes into vesicles. [ABSTRACT FROM AUTHOR]

Metal curved panels are commonly used in engineering structures, but they may be more susceptible to damage under impact loads compared to flat panels. Polyurea coating has been proposed as a solution to improve impact resistance. Therefore, this study investigates the impact resistance performance of curved composite panels by applying polyurea coating to aluminum‐based panels with different curvatures. First, a numerical model of polyurea‐coated aluminum composite panels was established using the finite element software LS‐DYNA, and the sensitivity of model mesh and the numerical model validity were carried out. Then, the impact resistance performance of polyurea‐coated aluminum‐based flat panels was studied from the aspects such as deformation modes and energy dissipation, and the influence of polyurea layer thickness and coating position on the impact resistance performance of polyurea‐coated aluminum composite panels was analyzed. Based on the above results, numerical models of polyurea‐coated aluminum‐based curved panels under different curvatures are further established, and the impact resistance performance of composite curved panels and the structural forms for effective protection against impact loads are comprehensively analyzed. The research results indicate that double‐sided polyurea coating is the optimal coating method for both aluminum flat panels and aluminum curved panels. After the coating thickness reaches 4 mm, there is no significant improvement in the structural impact resistance performance. The impact deformation of curved panels can be divided into four stages: dynamic buckling, plastic indentation, rebound deformation, and vibration. The concave surface has strong impact and deformation resistance, and the convex surface has strong impact resistance. The research results have important theoretical implications for the safe engineering design of protective structures using metal curved panels. [ABSTRACT FROM AUTHOR]

Curvature of carbon materials has gained significant attention as catalysts due to their distinctive properties and potential applications. This review comprehensively summarizes how the bending of carbon materials can improve electrocatalytic performance, with special attention to the applications of various bent carbon materials (such as carbon nanotubes, graphene, and fullerene) in electrocatalysts and a large number of related density functional theory (DFT) theoretical calculations. Extensive mechanism research has provided a wealth of evidence indicating that the curvature of carbon materials has a profound impact on catalytic activity. This improvement in catalytic performance by curved carbon materials is attributed to factors like a larger active surface area, modulation of electronic structure, and better dispersal of catalytic active sites. A comprehensive understanding and utilization of these effects enable the design of highly efficient carbon‐based catalysts for applications in energy conversion, environmental remediation, and chemical synthesis. [ABSTRACT FROM AUTHOR]

N‐coordinated Ni sites (NiNx) are effective catalysts for the electrochemical reduction of CO2 to CO. In most researches, modulating the coordination environment of Ni atoms is focused on to improve electrochemical CO2 reduction (ECR) performance. However, the influence of the carbon substrate's structure on the intrinsic activity of NiNx is seldom investigated. The highly curved surface of carbon nanotubes (CNT) may provide a unique curvature effect on NiNx. It is found that the Ni residues in CNT can be atomized to form NiNx sites on the surface of CNT (Ni‐N/CNT@covalent triazine framework [CTF]) through high‐temperature pyrolysis, using a soluble CTF nanosheet as N precursor. The π‐conjugated and ultrathin 2D structure of CTF enables closer interfacial contact between CTF and CNT, which avoids the formation of a thick carbon layer to maximize the curvature effect. Theoretical data reveal that the NiN3 configuration may act as a highly active ECR site, and the curvature effect from CNT can further tune the electronic structure of NiN3, thus improving the ECR kinetics. The Ni‐N/CNT@CTF‐based flow‐cell electrolyzer exhibits a jCO of 201 mA cm−2 at −0.9 V with a high FECO of 98%. [ABSTRACT FROM AUTHOR]

We develop a conformal duality for space‐like graphs in Riemannian and Lorentzian three‐manifolds that admit a Riemannian submersion over a Riemannian surface whose fibers are the integral curves of a Killing vector field, which is time‐like in the Lorentzian case. The duality swaps mean curvature and bundle curvature and sends the length of the Killing vector field to its reciprocal while keeping invariant the base surface. We obtain two consequences of this result. On the one hand, we find entire graphs in Lorentz–Minkowski space L3$\mathbb {L}^3$ with prescribed mean curvature a bounded function H∈C∞(R2)$H\in \mathcal {C}^\infty (\mathbb {R}^2)$ with bounded gradient. On the other hand, we obtain conditions for the existence and nonexistence of entire graphs which are related to a notion of the critical mean curvature. [ABSTRACT FROM AUTHOR]

Background: Sir Roy Calne in 1976 described "Biliary reconstruction is the Achilles heel of liver transplantation," and it remains true. In some patients, such as those with short‐gut syndrome and concomitant biliary atresia, neither duct to duct nor Roux biliary reconstruction is feasible. Methods: We present a case of child's third liver transplant (LT), where an innovative extra‐anatomical biliary bypass was created using a sleeve from greater curvature of the stomach. Results: The patient is well nearly 10 years following the LT. Conclusions: This technique could prove to be an important addition to the armamentarium of a surgeon in difficult retransplants and in patients with short‐gut syndrome as it provides a viable option with good long‐term outcome. [ABSTRACT FROM AUTHOR]

Background: Standard surgery for upper advanced gastric cancer without invasion of the greater curvature (UGC‐GC) is spleen‐preserving D2 total gastrectomy without dissection of the splenic‐hilar nodes (#10). However, some patients with nodal metastasis to #10 survive more than 5 years due to nodal dissection of #10. If nodal metastasis to #10 is predictable based on the positivity of other nodes dissected by the current standard surgery without #10 nodal dissection, physicians may be able to consider #10 dissection. Methods: This study retrospectively reviewed data from the National Cancer Center Hospital in Japan between 2000 and 2012. We selected cases that met the following criteria: (1) D2 or more total gastrectomy with splenectomy, (2) UGC‐GC, and (3) histological type is gastric adenocarcinoma. We performed univariate and multivariate analyses concerning lymph node stations associated with #10 metastasis. Results: A total of 366 patients were examined. A multivariate analysis revealed that #10 metastasis was associated with positivity of the nodes along the short gastric arteries (#4sa) and distal nodes along the splenic artery (#11d) (#4sa: p = 0.003, #11d: p = 0.016). When either key node was positive, the metastatic rate of #10 was 24.4%, and the therapeutic value index was 13.3. Conclusions: #4sa and #11d were key lymph nodes predicting #10 nodal metastasis in UGC‐GC. When these key nodes are positive on computed tomography before surgery or according to a rapid pathological examination during surgery, dissection of #10 should be considered even if upper advanced tumors are not invading the greater curvature. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the rigidity and vanishing properties of compact submanifolds with free boundary of arbitrary codimension in the unit ball. We first show that a minimal submanifold with free boundary in the unit ball satisfying a pointwise or integral curvature pinching condition on the second fundamental form is a flat equatorial disk. Then we prove a vanishing theorem for cohomology groups for submanifolds with free boundary in the unit ball under an integral curvature pinching condition on the trace‐free second fundamental form. [ABSTRACT FROM AUTHOR]