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Given a class of embeddings into a contact or a symplectic manifold, we give a sufficient condition, that we call isocontact or isosymplectic realization, for this class to satisfy a general h$h$‐principle. The flexibility follows from the h$h$‐principles for isocontact and isosymplectic embeddings, it provides a framework for classical results, and we give two new applications. Our main result is that embeddings transverse to a contact structure satisfy a full h$h$‐principle in two cases: if the complement of the embedding is overtwisted, or when the intersection of the image of the formal derivative with the contact structure is strictly contained in a proper symplectic subbundle. We illustrate the general framework on symplectic manifolds by studying the universality of Hamiltonian dynamics on regular level sets via a class of embeddings. [ABSTRACT FROM AUTHOR]

Rationale: Sublingual hematoma is a potentially lethal complication following mandibular implant placement. Due to the scarce cases reported, the management is controversial. In this article, a case is discussed focusing on the different treatment options to establish an orientative guideline. Patient Concerns: A patient with sublingual hematoma following implant surgery was urgently referred. Despite no active bleeding, breathing difficulty due to oropharyngeal obstruction and oxygen saturation decrease were present. Diagnosis: Stable sublingual hematoma with respiratory distress, based on clinical findings and observation. Treatment: Under local anaesthesia, percutaneous tracheostomy without previous intubation was performed for airway preservation. No surgical approach for the hematoma was made. Outcomes: Uneventful recovery with spontaneous resolution of the hematoma in few days. Takeaway Lessons: Anatomic knowledge of this area and proper surgical planning are required to avoid this complication. Regarding management, airway preservation is mandatory. Surgical approach for the bleeding source will depend on hematoma progression. [ABSTRACT FROM AUTHOR]

This paper contributes to the study of Engel structures and their classification. The main result introduces the notion of a loose family of Engel structures and shows that two such families are Engel homotopic if and only if they are formally homotopic. This implies a complete $h$ -principle when auxiliary data is fixed. As a corollary, we show that Lorentz and orientable Cartan prolongations are classified up to homotopy by their formal data. [ABSTRACT FROM AUTHOR]

A foliation is said to admit a foliated contact structure if there is a codimension $$1$$ distribution in the tangent space of the foliation such that the restriction to any leaf is contact. We prove a version of the Weinstein conjecture for Reeb vector fields in the presence of an overtwisted leaf. The result is shown to be sharp. [ABSTRACT FROM AUTHOR]

We construct positive loops of Legendrian submanifolds in several instances. In particular, we partially recover G. Liu's result stating that any loose Legendrian admits a positive loop, under some mild topological assumptions on the Legendrian. Moreover, we show contractibility of the constructed loops under an extra topological assumption. [ABSTRACT FROM AUTHOR]

Endoscopic full‐thickness resection (EFTR) is a “changing‐concept” endoscopic resection technique, which safely allows resecting deep submucosal tumors (SMTs) in the gastrointestinal (GI) wall. It's a highly promising endoscopic procedure that allows full‐thickness excision of a small piece of the complete GI wall by using only a flexible endoscope. EFTR is a meeting point between surgery and endoscopy and probably the onset of many prospective combined minimally invasive therapeutic techniques that science will explore. In this review, use of the EFTR technique for gastrointestinal SMTs is highlighted, focusing on some technical aspects, indications, contraindications and outcomes. [ABSTRACT FROM AUTHOR]

In this article, we introduce the topological study of codimension-1 foliations which admit contact structures on the leaves. A parametric existence h-principle for foliated contact structures is provided for any cooriented foliation in a closed oriented four-fold. [ABSTRACT FROM AUTHOR]

A Lefschetz hyperplane theorem for the determinantal loci of a morphism between two holomorphic vector bundles E and F over a complex manifold is proved, under the condition that E* ⊗ F is Griffiths k-positive. This result is applied to find some homotopy groups of the Brill–Noether loci for a generic curve. 2000 Mathematics Subject Classification 32Q55, 14M12, 14H51. [ABSTRACT FROM PUBLISHER]

We define Maslov-type indices associated to contact and symplectic transformation groups. There are two such families of indices. The first class of indices are maps from the homotopy groups of the contactomorphism or symplectomorphism group to a quotient of Z . These are based on a generalization of the Maslov index. The second class of indices are maps from the homotopy groups of the space of contact structures or the space of cohomologous symplectic forms to the homotopy groups of a simple homogeneous space. We provide a detailed construction and describe some properties of these indices and their applications. [ABSTRACT FROM AUTHOR]