Hyperbolic groups with planar boundaries

• 成果类型: Article
• 署名作者: Haissinsky, Peter
• 署名单位: Universite de Toulouse; Universite Toulouse III - Paul Sabatier
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0552-x
• 发表日期: 2015
• 页码: 239-307
• 关键词: kleinian-groups; accessibility; MANIFOLDS; SUBGROUPS; criterion; RIGIDITY

摘要

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.