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Theorem 4.1.3 shows that domains \(\mathcal {A}_r:=\{z \in \mathbb {C}:|z+1 / z|<2 r\}\) , where r is a constant greater than one, are the natural “standard” doubly connected domains. For the domains of higher connectivity, there is no natural unique choice of uniformizing domains. Instead, there are several somewhat standard families of canonical domains.

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Riemann Multiply Connected Domains

  • 章节

  • 发表日期：

    2025年

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  • Peter V. Dovbush,
  • Steven G. Krantz

摘要

Theorem 4.1.3 shows that domains \(\mathcal {A}_r:=\{z \in \mathbb {C}:|z+1 / z|<2 r\}\) , where r is a constant greater than one, are the natural “standard” doubly connected domains. For the domains of higher connectivity, there is no natural unique choice of uniformizing domains. Instead, there are several somewhat standard families of canonical domains.