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Uniform growth of groups acting on Cartan–Hadamard spaces

Gérard BessonGilles CourtoisSylvestre Gallot — 2011

Journal of the European Mathematical Society

In this paper we investigate the growth of finitely generated groups. We recall the definition of the algebraic entropy of a group and show that if the group is acting as a discrete subgroup of the isometry group of a Cartan–Hadamard manifold with pinched negative curvature then a Tits alternative is true. More precisely the group is either virtually nilpotent or has a uniform growth bounded below by an explicit constant.

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