2 citations · 3 across the 4 of their papers we have counts for
4 papers
Les géométries de Hilbert sont à géométrie locale bornée
Bruno Colbois, Constantin Vernicos
We prove that the Hilbert geometry of a convex domain in has bounded local geometry, i.e., for a given radius, all balls are bilipschitz to a euclidean domain of ${…
Capacite et inegalite de Faber-Krahn dans l'espace euclidien
Jerome Bertrand, Bruno Colbois
In this paper, we define a new capacity which allows us to control the behaviour of the Dirichlet spectrum of a compact Riemannian manifold with boundary, with "small" subsets (whi…
Bas du spectre et delta-hyperbolicité en géométrie de Hilbert plane
Bruno Colbois, Constantin Vernicos
We prove that the Hilbert geometry of a convex domain in the plane is Gromov hyperbolic, if, and only if, the bottom of its spectrum is not zero
L'aire des triangles ideaux en geometrie de Hilbert
Bruno Colbois, Constantin Vernicos, Patrick Verovic
In this paper we study the area of ideals triangles in a convex domain with its Hilbert geometry. We obtain a characterization of the hyperbolic geometry among all the Hilbert geom…