圆域的刚性定理
Rigidity theorems for circle domains
摘要：
黎曼球面上的圆域$Ω$是共形刚性的，如果从$Ω$到另一个圆域上的每个共形映射都是Möbius变换的限制.本文证明了满足Jones和Smirnov提出的拟双曲条件的圆域是共形刚性的。特别地，Hölder圆域和John圆域都是共形刚性的。这为He和Schramm关于刚性和共形可移动性的猜想提供了新的证据。
英文摘要：
A circle domain $Ω$ in the Riemann sphere is conformally rigid if every conformal map from $Ω$ onto another circle domain is the restriction of a Möbius transformation. We show that circle domains satisfying a certain quasihyperbolic condition, which was considered by Jones and Smirnov, are conformally rigid. In particular, Hölder 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.
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