Conformal welding and Koebe's theorem

• 成果类型: Article
• 署名作者: Bishop, Christopher J.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2007.166.613
• 发表日期: 2007
• 页码: 613-656
• 关键词: sewing functions; circle packings; CURVES; uniformization; MAPS; continua; points; plane; sets

摘要

It is well known that not every orientation-preserving homeomorphisin of the circle to itself is a conformal welding, but in this paper we prove several results which state that every homeomorphism is almost a welding in a precise way. The proofs are based on Koebe's circle domain theorem. We also give a new proof of the well known fact that quasisymmetric maps are conformal weldings.