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Colbois, Bruno
Résultat de la recherche
Hilbert geometry for convex polygonal domains
2011-1-21, Colbois, Bruno, Vernicos, Constantin, Verovic, Patrick
Bas du spectre et delta-hyperbolicité en géométrie de Hilbert plane
2006-12-21, Colbois, Bruno, Vernicos, Constantin
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.
Area of ideal triangles and Gromov hyperbolicity in Hilbert Geometry
2008, Colbois, Bruno, Vernicos, Constantin, Verovic, Patrick
L'aire des triangles idéaux en géométrie de Hilbert
2004-12-20, Colbois, Bruno, Vernicos, Constantin, Verovic, Patrick
Les géométries de Hilbert sont à géométrie locale bornée
2007-12-21, Colbois, Bruno, Vernicos, Constantin
We prove that the Hilbert geometry of a convex domain in R-n has bounded local geometry, i.e., for a given radius, all balls are bilipschitz to a euclidean domain of R-n. As a consequence, if the Hilbert geometry is also Gromov hyperbolic, then the bottom of its spectrum is strictly positive. We also give a counter exemple in dimension three wich shows that the reciprocal is not true for non plane Hilbert geometries.