Rigidity theorems for circle domains

• 成果类型: Article
• 署名作者: Ntalampekos, Dimitrios; Younsi, Malik
• 署名单位: State University of New York (SUNY) System; Stony Brook University; University of Hawaii System; University of Hawaii Manoa
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-019-00921-1
• 发表日期: 2020
• 页码: 129-183
• 关键词: koebe uniformization; removability; sets

摘要

A circle domain omega\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega $$\end{document} in the Riemann sphere is conformally rigid if every conformal map from omega\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega $$\end{document} onto another circle domain is the restriction of a Mobius transformation. We show that circle domains satisfying a certain quasihyperbolic condition, which was considered by Jones and Smirnov (Ark Mat 38, 263-279, 2000), are conformally rigid. In particular, Holder circle domains and John circle domains are all conformally rigid. This provides new evidence for a conjecture of He and Schramm relating rigidity and conformal removability.