Dougall, Rhiannon and Sharp, Richard (2016) Amenability, critical exponents of subgroups and growth of closed geodesics. Mathematische Annalen, 365 (3-4). pp. 1359-1377. doi:10.1007/s00208-015-1338-1 ISSN 0025-5831.

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Abstract

Let Γ be a (non-elementary) convex co-compact group of isometries of a pinched Hadamard manifold X. We show that a normal subgroup Γ0 has critical exponent equal to the critical exponent of Γ if and only if Γ/Γ0 is amenable. We prove a similar result for the exponential growth rate of closed geodesics on X/Γ. 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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Geodesics (Mathematics)
Journal or Publication Title:	Mathematische Annalen
Publisher:	Springer Verlag
ISSN:	0025-5831
Official Date:	August 2016
Dates:	Date Event August 2016 Published 11 December 2015 Available 27 November 2015 Accepted 30 April 2015 Submitted
Volume:	365
Number:	3-4
Page Range:	pp. 1359-1377
DOI:	10.1007/s00208-015-1338-1
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access (Creative Commons)
Date of first compliant deposit:	28 January 2016
Date of first compliant Open Access:	28 January 2016

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