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* Corresponding author 1 Picard IMT - Institut de Mathématiques de Toulouse UMR5219

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 CAT0 cube complex.

Keywords : conformal gauge sewing cube complexes hyperbolic $3$-manifolds convex-cocompact Kleinian groups JSJ-decomposition quasisymmetric maps Hyperbolic groups

Author: Peter Haïssinsky -

Source: https://hal.archives-ouvertes.fr/


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