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Discrete subgroups of small critical exponent

Beibei Liu and Shi Wang

Geometry & Topology 27 (2023) 2347–2381
Abstract

We prove that finitely generated Kleinian groups Γ < Isom (n) with small critical exponent are always convex cocompact. We also prove some geometric properties for any complete pinched negatively curved manifold with critical exponent less than 1.

Keywords
discrete subgroups, critical exponent, convex compactness
Mathematical Subject Classification
Primary: 22E40
Secondary: 20F65
References
Publication
Received: 17 May 2021
Revised: 19 March 2022
Accepted: 2 April 2022
Published: 25 August 2023
Proposed: David Gabai
Seconded: David Fisher, Benson Farb
Authors
Beibei Liu
Department of Mathematics
The Ohio State University
Columbus, OH
United States
Shi Wang
Institute of Mathematical Sciences
ShanghaiTech University
Shanghai
China

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