Koebe uniformization of nondegenerate domains with bounded gap-ratios

Koebe uniformization is a fundemental problem in complex analysis. In this paper, we use the transboundary extremal length to show that every nondegenerate and uncountably connected domain with a bounded gap-ratio is conformally equivalent to a circle domain.

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Publication Details

Journal
Proceedings of the American Mathematical Society
Published
2026-01-14
DOI
https://doi.org/10.1090/proc/17564
Primary Topic
Analytic and geometric function theory
Type
article
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article

Koebe uniformization of nondegenerate domains with bounded gap-ratios

Yi Zhong
Proceedings of the American Mathematical Society
Analytic and geometric function theory
article

Koebe uniformization of nondegenerate domains with bounded gap-ratios

Yi Zhong
article en

Abstract

Koebe uniformization is a fundemental problem in complex analysis. In this paper, we use the transboundary extremal length to show that every nondegenerate and uncountably connected domain with a bounded gap-ratio is conformally equivalent to a circle domain.

Proceedings of the American Mathematical SocietyVol. 154(4)
Ningbo University (CN), Ningbo University of Technology (CN)
Reduced inequalities
Openalex Percentile: Top 84%
Analytic and geometric function theory
DOISourceOpenAlex
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Koebe uniformization of nondegenerate domains with bounded gap-ratios — Yi Zhong · Proceedings of the American Mathematical Society (2026) | TGRS Research Map | TGRS