Margulis Lemma with no curvature and growth of groups
Gérard Besson and Gilles Courtois

We will recall the Margulis-Zassenhaus lemma in hyperbolic space and its generalisation to the case of variable curvature. We will establish a version where the assumption on the curvature is replaced by an assumption on the entropy. We will present some applications, for instance a ``precompactness theorem'' without any assumption on the curvature. The proof of this theorem relies in particular on the study of the uniform growth of certain groups.



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