{"title":"Extension of planar Hölder homeomorphisms","authors":"Stanislav Hencl, Aleksis Koski","doi":"10.1112/jlms.12970","DOIUrl":null,"url":null,"abstract":"<p>Let <span></span><math>\n <semantics>\n <mrow>\n <mi>α</mi>\n <mo>∈</mo>\n <mo>(</mo>\n <mn>0</mn>\n <mo>,</mo>\n <mn>1</mn>\n <mo>)</mo>\n </mrow>\n <annotation>$\\alpha \\in (0,1)$</annotation>\n </semantics></math>. We show that any <span></span><math>\n <semantics>\n <mi>α</mi>\n <annotation>$\\alpha$</annotation>\n </semantics></math>-Hölder homeomorphism from the unit circle in the plane to the plane can be extended to an <span></span><math>\n <semantics>\n <mi>α</mi>\n <annotation>$\\alpha$</annotation>\n </semantics></math>-Hölder homeomorphism from the whole unit disc.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"110 3","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the London Mathematical Society-Second Series","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/jlms.12970","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let . We show that any -Hölder homeomorphism from the unit circle in the plane to the plane can be extended to an -Hölder homeomorphism from the whole unit disc.
期刊介绍：
The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.
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