On étudie la notion de finitude géométrique pour certaines géométries de Hilbert définies par un ouvert strictement convexe à bord de classe ${𝒞}^1$.La définition dans le cadre des espaces Gromov-hyperboliques fait intervenir l’action du groupe discret considéré sur le bord de l’espace. On montre, en construisant explicitement un contre-exemple, que cette définition doit être renforcée pour obtenir des définitions équivalentes en termes de la géométrie de l’orbifold quotient, similaires à celles obtenues...

We prove the Finsler analog of the conformal Lichnerowicz-Obata conjecture showing that a complete and essential conformal vector field on a non-Riemannian Finsler manifold is a homothetic vector field of a Minkowski metric.

The structure of complex Finsler manifolds is studied when the Finsler metric has the property of the Kobayashi metric on convex domains: (real) geodesics locally extend to complex curves (extremal disks). It is shown that this property of the Finsler metric induces a complex foliation of the cotangent space closely related to geodesics. Each geodesic of the metric is then shown to have a unique extension to a maximal totally geodesic complex curve Σ which has properties of extremal disks. Under...

The paper is concerned with the graph formulation of forced anisotropic mean curvature flow in the context of the heteroepitaxial growth of quantum dots. The problem is generalized by including anisotropy by means of Finsler metrics. A semi-discrete numerical scheme based on the method of lines is presented. Computational results with various anisotropy settings are shown and discussed.

The aim of this paper is to construct a canonical nonlinear connection $\Gamma =(M_{\left(\alpha \right)\beta }^{\left(i\right)},N_{\left(\alpha \right)j}^{\left(i\right)})$ on the 1-jet space $J^1(T,M)$ from the Euler-Lagrange equations of the quadratic multi-time Lagrangian function $$L=h^{\alpha \beta }\left(t\right)g_{ij}(t,x)x_{\alpha }^i{x}_{\beta }^j+U_{\left(i\right)}^{\left(\alpha \right)}(t,x)x_{\alpha }^i+F(t,x).$$