Hyperbolic groups with planar boundaries

Hyperbolic groups with planar boundaries

We prove that the class of convex-cocompact Kleinian groups is quasi-isometrically rigid. We also establish that a word hyperbolic group with a planar boundary different from the sphere is virtually a convex-cocompact Kleinian group provided that its boundary has Ahlfors regular conformal dimension...

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Bibliographic Details
Main Author: Haïssinsky, Peter
Format: Journal Article
Language:English
Published: 09-02-2013
Subjects:
Mathematics - Group Theory
Mathematics - Metric Geometry
Online Access:Get full text
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Summary:We prove that the class of convex-cocompact Kleinian groups is quasi-isometrically rigid. We also establish that a word hyperbolic group with a planar boundary different from the sphere is virtually a convex-cocompact Kleinian group provided that its boundary has Ahlfors regular conformal dimension strictly less than $2$ or if it acts geometrically on a CAT(0) cube complex.
DOI:10.48550/arxiv.1302.2219