{"title":"平面赫尔德同构的扩展","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":1.2000,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12970","citationCount":"0","resultStr":"{\"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\":1.2000,\"publicationDate\":\"2024-08-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12970\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the London Mathematical Society-Second Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://londmathsoc.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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the London Mathematical Society-Second Series","FirstCategoryId":"100","ListUrlMain":"https://londmathsoc.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}
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
