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Journal Articles Inventiones Mathematicae Year : 2015

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 strictly less than $2$ or if it acts geometrically on a CAT(0) cube complex.
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Dates and versions

hal-00786453 , version 1 (08-02-2013)
hal-00786453 , version 2 (23-05-2014)



Peter Haïssinsky. Hyperbolic groups with planar boundaries. Inventiones Mathematicae, 2015, 201 (no. 1), pp.239 -- 307. ⟨hal-00786453v2⟩
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