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• W1492891963 abstract "Let $$Gamma $$ be a (non-elementary) convex co-compact group of isometries of a pinched Hadamard manifold X. We show that a normal subgroup $$Gamma _0$$ has critical exponent equal to the critical exponent of $$Gamma $$ if and only if $$Gamma /Gamma _0$$ is amenable. We prove a similar result for the exponential growth rate of closed geodesics on $$X/Gamma $$ . These statements are analogues of classical results of Kesten for random walks on groups and Brooks for the spectrum of the Laplacian on covers of Riemannian manifolds." @default.
• W1492891963 created "2016-06-24" @default.
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• W1492891963 date "2015-12-11" @default.
• W1492891963 modified "2023-10-17" @default.
• W1492891963 title "Amenability, critical exponents of subgroups and growth of closed geodesics" @default.
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• W1492891963 doi "https://doi.org/10.1007/s00208-015-1338-1" @default.
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