Conformal dimension and Gromov hyperbolic groups with 2–sphere boundary

Bonk, Mario; Kleiner, Bruce

doi:10.2140/gt.2005.9.219

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

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 $\partial_{\infty} G$ 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 $ℍ^{3}$ .

Keywords

Gromov hyperbolic groups, Cannon's conjecture, quasisymmetric maps

Mathematical Subject Classification 2000

Primary: 20F67

Secondary: 30C65

References

Forward citations

Publication

Received: 28 July 2003

Revised: 3 April 2004

Accepted: 9 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

Volume 9, issue 1 (2005)