Uniform growth of groups acting on Cartan-Hadamard spaces

Besson, Gérard; Courtois, Gilles; Gallot, Sylvain

Uniform growth of groups acting on Cartan-Hadamard spaces

Authors

Besson, Gérard

Courtois, Gilles

Gallot, Sylvain

Description

Let $X$ be an $n$-dimensional simply connected manifold of pinched sectional curvature $-a^2 \leq K \leq -1$. There exist a positive constant $C(n,a)$ such that for any finitely generated discrete group $Γ$ acting on $X$, then either $Γ$ is virtually nilpotent or the algebraic entropy $Ent (Γ) \geq C(n,a)$.