DEFINITIONS OF QUASICONFORMALITY

• 成果类型: Article
• 署名作者: HEINONEN, J; KOSKELA, P
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/BF01241122
• 发表日期: 1995
• 页码: 61-79
• 关键词: carnot-caratheodory metrics; mappings; SPACES

摘要

We establish that the infinitesimal ''H-definition'' for quasiconformal mappings on Carnot groups implies global quasisymmetry, and hence the absolute continuity on almost all lines. Our method is new even in R(n) where we obtain that the ''limsup'' condition in the H-definition can be replaced by a ''liminf'' condition. This leads to a new removability result for (quasi)conformal mappings in Euclidean spaces. An application to parametrizations of chord-are surfaces is also given.