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G&T Monographs |
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Conformal dimension and Gromov hyperbolic groups with
2–sphere boundary
Mario Bonk and Bruce Kleiner
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Geometry & Topology 9 (2005)
219–246
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Abstract
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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.
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Keywords
Gromov hyperbolic groups, Cannon's
conjecture, quasisymmetric maps
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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
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