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Mickaël Crampon; Ludovic Marquis
Un lemme de Kazhdan-Margulis-Zassenhaus pour les géométries de Hilbert
(A Kazhdan-Margulis-Zassenhaus lemma for Hilbert geometry)
Annales mathématiques Blaise Pascal, 20 no. 2 (2013), p. 363-376, doi: 10.5802/ambp.330
Article PDF | Reviews MR 3138033 | Zbl 1282.22007
Class. Math.: 22E40, 22F50, 57M99
Keywords: Hilbert’s geometry, lemma of Margulis, action geometrically finite

Résumé - Abstract

We prove a Kazhdan-Margulis-Zassenhaus lemma for Hilbert geometries. More precisely, in every dimension $n$ there exists a constant $\varepsilon _n > 0$ such that, for any properly convex open set $\Omega $ and any point $x \in \Omega $, any discrete group generated by a finite number of automorphisms of $\Omega $, which displace $x$ at a distance less than $\varepsilon _n$, is virtually nilpotent.

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