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SubRiemannian geodesics induced by the Grushin operatorare obtained and completely classified. The classification is done with respect to the position of the endpoints of the geodesics. The number of geodesics starting at the origin is determined, for the finite case, and the number of intersection points of an arbitrary geodesic with the canonical submanifolds is found as well. [ABSTRACT FROM PUBLISHER]

Geometric properties of graphs of solutions for the quartic interaction PDE are studied in the present work. Two classes of solutions are considered. One class is represented by soliton solutions, whereas the other class consists of solutions of a first order PDE system, which generates the quartic interaction PDE, in the sense of least squares type action. We prove that for both classes the graphs of solutions are Tzitzeica at, i.e., the associated Tzitzeica curvature tensor vanishes. It is also shown how the quartic interaction PDE can be generated using a least squares type action. [ABSTRACT FROM AUTHOR]

We study the boundedness of the Dirichlet energy of moving frames associated to immersions of torus in the Poincaré upper half-space. The frame energy functional is closely related to the Willmore energy and also to the conformal structure on the underlying torus. A lower bound for the frame energy is established. [ABSTRACT FROM AUTHOR]

We study the boundedness of the Dirichlet energy of moving frames associated to immersions of torus in the Poincaré upper half-space. The frame energy functional is closely related to the Willmore energy and also to the conformal structure on the underlying torus. A lower bound for the frame energy is established. [ABSTRACT FROM AUTHOR]

We study the boundedness of the Dirichlet energy of moving frames associated to immersions of torus in the Poincaré upper half-space. The frame energy functional is closely related to the Willmore energy and also to the conformal structure on the underlying torus. A lower bound for the frame energy is established. [ABSTRACT FROM AUTHOR]

In this paper we study a new iterative scheme for mappings satisfying a condition weaker than Suzuki's generalized nonexpansiveness, defined on CAT(0) spaces. More precisely, we obtain strong convergence results and establish the Δ-convergence of the resulting iterate sequence. [ABSTRACT FROM AUTHOR]