Résumé
Annales de l'Institut Fourier 57, 4 (2007) 1359-1375 We prove that the Hilbert geometry of a convex domain in${\mathbb R}^n$has bounded local geometry, i.e., for a given radius, all balls are bilipschitz to a euclidean domain of${\mathbb R}^n$ . 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 which shows that the reciprocal is not true for non plane Hilbert geometries.