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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Veröffentlicht in:Inventiones mathematicae 2015-07, Vol.201 (1), p.239-307
1. Verfasser: Haïssinsky, Peter
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Sprache:eng
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Group Theory
Mathematics
Mathematics and Statistics
Metric Geometry
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description 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.
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Mathematics
Mathematics and Statistics
Metric Geometry
title Hyperbolic groups with planar boundaries
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