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Les géométries de Hilbert sont à géométrie locale bornée
Auteur(s)
Vernicos, Constantin
Date de parution
2007-12-21
In
Annales de l'Institut Fourier
Vol.
4
No
57
De la page
1359
A la page
1375
Résumé
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.
Identifiants
Type de publication
journal article
