{"title":"具有有界间隙率的非enerate域的柯贝均匀化","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":"{\"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}","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}
Koebe uniformization of nondegenerate domains with bounded gap-ratio
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.