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Conformal dimension and Gromov hyperbolic groups with 2–sphere boundary

Mario Bonk and Bruce Kleiner

Geometry & Topology 9 (2005) 219–246

DOI: 10.2140/gt.2005.9.219

arXiv: math.GR/0208135
Abstract

Suppose G is a Gromov hyperbolic group, and ∂∞ G is quasisymmetrically homeomorphic to an Ahlfors Q–regular metric 2–sphere Z with Ahlfors regular conformal dimension Q. Then G acts discretely, cocompactly, and isometrically on H3.

Keywords

Gromov hyperbolic groups, Cannon's conjecture, quasisymmetric maps
Mathematical Subject Classification

Primary: 20F67

Secondary: 30C65
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Publication

Received: 28 July 2003
Revised: 3 April 2004
Accepted: 09 December 2004
Published: 26 January 2005
Proposed: David Gabai
Seconded: Jean-Pierre Otal, Walter Neumann
Authors
Mario Bonk
Department of Mathematics
University of Michigan
Ann Arbor
Michigan 48109-1109
USA
Bruce Kleiner
Department of Mathematics
University of Michigan
Ann Arbor
Michigan 48109-1109
USA