Conformal dimension and Gromov hyperbolic groups with 2-sphere boundary

Mario Bonk; Bruce Kleiner

doi:10.2140/gt.2005.9.219

Conformal dimension and Gromov hyperbolic groups with 2-sphere boundary

Mario Bonk, Bruce Kleiner

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	219-246
Number of pages	28
Journal	Geometry and Topology
Volume	9
DOIs	https://doi.org/10.2140/gt.2005.9.219
State	Published - Jan 26 2005

Keywords

Cannon's conjecture
Gromov hyperbolic groups
Quasisymmetric maps

ASJC Scopus subject areas

Geometry and Topology

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10.2140/gt.2005.9.219

Cite this

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title = "Conformal dimension and Gromov hyperbolic groups with 2-sphere boundary",

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 = "Cannon's conjecture, Gromov hyperbolic groups, Quasisymmetric maps",

author = "Mario Bonk and Bruce Kleiner",

year = "2005",

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doi = "10.2140/gt.2005.9.219",

language = "English (US)",

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issn = "1465-3060",

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T1 - Conformal dimension and Gromov hyperbolic groups with 2-sphere boundary

AU - Bonk, Mario

AU - Kleiner, Bruce

PY - 2005/1/26

Y1 - 2005/1/26

N2 - 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.

AB - 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.

KW - Cannon's conjecture

KW - Gromov hyperbolic groups

KW - Quasisymmetric maps

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U2 - 10.2140/gt.2005.9.219

DO - 10.2140/gt.2005.9.219

M3 - Article

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EP - 246

JO - Geometry and Topology

JF - Geometry and Topology

ER -

Conformal dimension and Gromov hyperbolic groups with 2-sphere boundary

Abstract

Keywords

ASJC Scopus subject areas

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