Rigidity and continuous extension for conformal maps of circle domains
نویسندگان
چکیده
We present sufficient conditions so that a conformal map between planar domains whose boundary components are Jordan curves or points has continuous homeomorphic extension to the closures of domains. Our involve notions cofat and C N E D CNED sets, i.e., countably negligible for extremal distances, recently introduced by author. use this result towards establishing rigidity class circle A domain is conformally rigid if every onto another restriction Möbius transformation. show point rigid. This strongest among all earlier works provides substantial evidence conjecture He–Schramm [Invent. Math. 115 (1994), no. 2, 297–310], relating problems removability.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2023
ISSN: ['2330-0000']
DOI: https://doi.org/10.1090/tran/8923