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arXiv · 1302.2219

Hyperbolic groups with planar boundaries

Peter Haïssinsky
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Abstract

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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Peter Haïssinsky. 2013-02-09. Hyperbolic groups with planar boundaries. https://arxiv.org/abs/1302.2219

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