RIGIDITY OF CIRCLE DOMAINS WHOSE BOUNDARY HAS SIGMA-FINITE LINEAR MEASURE

• 成果类型: Article
• 署名作者: HE, ZX; SCHRAMM, O
• 署名单位: Weizmann Institute of Science
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/BF01231761
• 发表日期: 1994
• 页码: 297-310
• 关键词: packings

摘要

Let Q be a circle domain in the Riemann sphere C whose boundary has sigma-finite linear measure. We show that OMEGA is rigid in the sense that any conformal homeomorphism of Q onto any other circle domain is equal to the restriction of a Mobius transformation. Previously, Kaufman and Bishop have independently found examples of non-rigid circle domains whose boundary is a Cantor set of (Hausdorff) dimension one.