A SierpiAski carpet with the co-Hopfian property

• 成果类型: Article
• 署名作者: Merenkov, Sergei
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-010-0231-5
• 发表日期: 2010
• 页码: 361-388
• 关键词: hyperbolic groups; RIGIDITY

摘要

Motivated by questions in geometric group theory we define a quasisymmetric co-Hopfian property for metric spaces and provide an example of a metric SierpiAski carpet with this property. As an application we obtain a quasi-isometrically co-Hopfian Gromov hyperbolic space with a SierpiAski carpet boundary at infinity. In addition, we give a complete description of the quasisymmetry group of the constructed SierpiAski carpet. This group is uncountable and coincides with the group of bi-Lipschitz transformations.