{"title":"The Hausdorff dimension of planar elliptic measures via quasiconformal mappings","authors":"Ignasi Guillén-Mola","doi":"arxiv-2407.21145","DOIUrl":null,"url":null,"abstract":"In this paper we study the dimension of planar elliptic measures via the\napplication of quasiconformal mappings. In fact, in our case studies, we find a\nquasiconformal mapping that relates the elliptic measure in a domain to the\nharmonic measure in its image domain, and we deduce bounds for the Hausdorff\ndimension of the elliptic measure by the known results on the harmonic side.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"31 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Classical Analysis and ODEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.21145","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
In this paper we study the dimension of planar elliptic measures via the
application of quasiconformal mappings. In fact, in our case studies, we find a
quasiconformal mapping that relates the elliptic measure in a domain to the
harmonic measure in its image domain, and we deduce bounds for the Hausdorff
dimension of the elliptic measure by the known results on the harmonic side.
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