Conformal dimension and Gromov hyperbolic groups with 2-sphere boundary

Mario Bonk, Bruce Kleiner

Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
Pages (from-to)219-246
Number of pages28
JournalGeometry and Topology
Volume9
DOIs
StatePublished - Jan 26 2005

Keywords

  • Cannon's conjecture
  • Gromov hyperbolic groups
  • Quasisymmetric maps

ASJC Scopus subject areas

  • Geometry and Topology

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