Abstract

We consider the simplest class of countably connected domains with the unique limit point boundary component. We find the domains in this class where the limit component is simultaneously perfect in the Grötzsch sense, i.e. corresponds to a point boundary component under any conformal mapping, and regular in the sense of the Dirichlet problem. We call the regular point the Wiener point in commemoration of the role played by the legendary Wiener criterion in our study.

中文翻译：

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关于Grötzsch-Wiener点的存在

摘要

我们考虑具有唯一极限点边界分量的最简单类的可数连接域。我们在此类领域中发现，在Grötzsch意义上，极限分量同时是完美的，即对应于任何共形映射下的点边界分量，并且在Dirichlet问题的意义上是规则的。为了纪念传说中的维纳准则在我们的研究中所扮演的角色，我们将常规点称为维纳点。