Uniform growth of groups acting on Cartan-Hadamard spaces

Details Uniform growth of groups acting on Cartan-Hadamard spaces Uniform growth of groups acting on Cartan-Hadamard spaces

2008-10-17

arxiv.org/abs/0810.3151v1

Mathematics

Differential Geometry

Scientific paper

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 $\Gamma$ acting on $X$, then
either $\Gamma$ is virtually nilpotent or the algebraic entropy $Ent (\Gamma)
\geq C(n,a)$.

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