发表机构
Aristotle University of Thessaloniki; University of Hawaii Manoa（色雷斯大学; 夏威夷大学马诺阿分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文综述了黎曼球面上圆域的共形刚性研究进展，探讨其与Koebe猜想及共形可去除性的联系，并指出当前面临的挑战。
AI 中文摘要
黎曼球面上的一个域被称为“圆域”，如果其边界的每个连通分量要么是一个圆，要么是一个单点。如果一个圆域到另一个圆域的每个共形映射都是莫比乌斯变换的限制，则该圆域是“共形刚性的”。共形刚性与Koebe猜想密切相关，该猜想断言黎曼球面上的每个域都共形等价于一个圆域。在本文中，我们综述了共形刚性的近期进展，特别强调其与共形可去除性之间的关系。
英文摘要
A domain in the Riemann sphere is called a \textit{circle domain} if every connected component of its boundary is either a round circle or a single point. A circle domain is \textit{conformally rigid} if every conformal map onto another circle domain is the restriction of a Möbius transformation. Conformal rigidity is closely related to Koebe's conjecture, which asserts that every domain in the Riemann sphere is conformally equivalent to a circle domain. In this article, we survey recent progress on conformal rigidity, with particular emphasis on its relationship with conformal removability.
CommentsTo appear in Proceedings of the 2026 International Congress of Basic Science
