{"title":"Koebe uniformization of nondegenerate domains with bounded gap-ratio","authors":"Yi Zhong","doi":"arxiv-2408.03484","DOIUrl":null,"url":null,"abstract":"Koebe uniformization is a fundemental problem in complex analysis. In this\npaper, we use transboundary extremal length to show that every nondegenerate\nand uncountably connected domain with bounded gap-ratio is conformally\nhomeomorphic to a circle domain.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"15 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Complex Variables","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.03484","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Koebe uniformization is a fundemental problem in complex analysis. In this
paper, we use transboundary extremal length to show that every nondegenerate
and uncountably connected domain with bounded gap-ratio is conformally
homeomorphic to a circle domain.
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