Amenability, critical exponents of subgroups and growth of closed geodesics

作者：Dougall Rhiannon; Sharp Richard^*

来源：Mathematische Annalen, 2016, 365(3-4): 1359-1377.

DOI：10.1007/s00208-015-1338-1

Let be a (non-elementary) convex co-compact group of isometries of a pinched Hadamard manifold X. We show that a normal subgroup has critical exponent equal to the critical exponent of if and only if is amenable. We prove a similar result for the exponential growth rate of closed geodesics on . 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.

• 出版日期2016-8