论文标题
圆形结构域共形图的刚性和连续扩展
Rigidity and continuous extension for conformal maps of circle domains
论文作者
论文摘要
我们提出足够的条件，以便在边界组件是约旦曲线或点的平面域之间的共形图具有连续或同构延伸到域的闭合。我们的条件涉及COFAT域和CNED集的概念，即作者最近引入的极端距离可以忽略不计。我们将此结果用于建立一类圆形域的保形刚度。如果在另一个圆形域上的每个共形图是Möbius变换的限制，则圆形结构域是刚性的。我们表明，圆形边界组件被c的圆形域在形式上是刚性的。该结果是所有早期作品中最强大的结果，并为He-Schramm的刚性猜想提供了大量证据，从而将保形刚性和可移动性问题联系起来。
We present sufficient conditions so that a conformal map between planar domains whose boundary components are Jordan curves or points has a continuous or homeomorphic extension to the closures of the domains. Our conditions involve the notions of cofat domains and CNED sets, i.e., countably negligible for extremal distance, recently introduced by the author. We use this result towards establishing conformal rigidity of a class of circle domains. A circle domain is conformally rigid if every conformal map onto another circle domain is the restriction of a Möbius transformation. We show that circle domains whose point boundary components are CNED are conformally rigid. This result is the strongest among all earlier works and provides substantial evidence towards the rigidity conjecture of He-Schramm, relating the problems of conformal rigidity and removability.
