论文标题
极性集互补的保形刚度
Conformal Rigidity of Polar Set Complements
论文作者
论文摘要
令$ e $为$ \ mathbb {c} $的封闭极性子集。在此简短说明中，我们使用基本潜在理论工具来表明$ \ Mathbb {C} \ setMinus {e} $上的任何共形映射必然是Möbius地图。结果，我们得到的是，封闭极性集合$ e $的补充的共形自动形态是Möbius集团的离散子组，提供了$ \ lvert e \ rvert \ ge 2 $。
Let $E$ be a closed polar subset of $\mathbb{C}$. In this short note, we use elementary potential theoretic tools to show that any conformal map on $\mathbb{C}\setminus{E}$ is necessarily a Möbius map. As a consequence we obtain that the group of conformal automorphisms of the complement of a closed polar set $E$ is a discrete subgroup of the Möbius group, provided $\lvert E \rvert \ge 2$.
