Divergence groups have the Bowen property

• 成果类型: Article
• 署名作者: Bishop, CJ
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/3062115
• 发表日期: 2001
• 页码: 205-217
• 关键词: limit-sets; Hausdorff Dimension; kleinian-groups; harmonic measure; mostow rigidity; julia curves; length

摘要

We show that every deformation of a divergence-type Fuchsian group has a limit set which is either a circle or has dimension strictly larger than 1. This is known to be false for all convergence-type groups, and hence solves Bowen's problem in the general case. The proof uses a theorem of Dennis Sullivans about convex hulls in hyperbolic 3-space and we give a new, simpler proof of this result as well.