Demonstrates the conformal equivalence of nondegenerate domains with bounded gap-ratios to circle domains, indicating a fundamental relationship in complex analysis.
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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Yi Zhong (2026) studied this question.
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