Two properties of volume growth entropy in Hilbert geometry

The aim of this paper is to provide two examples in Hilbert geometry which show that volume growth entropy is not always a limit on the one hand, and that it may vanish for a non-polygonal domain in the plane on the other hand

Hilbert domains quasi-isometric to normed vector spaces

We prove that a Hilbert domain which is quasi-isometric to a normed vector space is actually a convex polytope

Rigidity of Hilbert metrics

We study the groups of isometries for Hilbert metrics on bounded open convex domains in n and show that if is such a set with a strictly convex boundary, the Hilbert geometry is asymptotically Riemannian at infinity. As a consequence of this result, we prove there are no Hausdorff quotients of by isometry subgroups with finite volume except when ∂ is an ellipsoi

Two properties of volume growth entropy in Hilbert geometry

The aim of this paper is to provide two examples in Hilbert geometry which show that volume growth entropy is not always a limit on the one hand, and that it may vanish for a non-polygonal domain in the plane on the other hand

Hilbert domains that admit a quasi-isometric embedding into Euclidean space

We prove that a Hilbert domain which admits a quasi-isometric embedding into a finite-dimensional normed vector space is actually a convex polytop

Area of ideal triangles and Gromov hyperbolicity in Hilbert Geometry

International audienceWe prove, in the context of Hilbert geometry, the equivalence between the existence of an upper bound on the area of ideal triangles and the Gromov-hyperbolicity

Hilbert geometry for convex polygonal domains

We prove in this paper that the Hilbert geometry associated with an open convex polygonal set is Lipschitz equivalent to Euclidean plane

Hyperbolicité au sens de Gromov et aires des triangles idéaux en géométrie de Hilbert

National audienc

Introduction à la géométrie de Hilbert

National audienc