Hyperbolic groups with planar boundaries
Group Theory
2014-05-26 v2 Metric Geometry
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 or if it acts geometrically on a CAT(0) cube complex.
Cite
@article{arxiv.1302.2219,
title = {Hyperbolic groups with planar boundaries},
author = {Peter Haïssinsky},
journal= {arXiv preprint arXiv:1302.2219},
year = {2014}
}
Comments
This new version contains a proof of the quasi-isometric rigidity of the class of convex-cocompact Kleinian groups. The structure of the text has been reorganized