#### Volume 9, issue 1 (2005)

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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
 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
Primary: 20F67
Secondary: 30C65