{"title":"半代数曲面的全局bi-Lipschitz分类","authors":"A. Fernandes, J. E. Sampaio","doi":"10.2422/2036-2145.202206_005","DOIUrl":null,"url":null,"abstract":"We classify semi-algebraic surfaces in $\\mathbb{R}^n$ with isolated singularities up to bi-Lipschitz homeomorphisms with respect to the inner distance. In particular, we obtain complete classifications for the Nash surfaces and the complex algebraic curves. We also address the minimal surfaces with finite total curvature.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"107 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Global bi-Lipschitz classification of semialgebraic surfaces\",\"authors\":\"A. Fernandes, J. E. Sampaio\",\"doi\":\"10.2422/2036-2145.202206_005\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We classify semi-algebraic surfaces in $\\\\mathbb{R}^n$ with isolated singularities up to bi-Lipschitz homeomorphisms with respect to the inner distance. In particular, we obtain complete classifications for the Nash surfaces and the complex algebraic curves. We also address the minimal surfaces with finite total curvature.\",\"PeriodicalId\":8132,\"journal\":{\"name\":\"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE\",\"volume\":\"107 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-12-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2422/2036-2145.202206_005\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2422/2036-2145.202206_005","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Global bi-Lipschitz classification of semialgebraic surfaces
We classify semi-algebraic surfaces in $\mathbb{R}^n$ with isolated singularities up to bi-Lipschitz homeomorphisms with respect to the inner distance. In particular, we obtain complete classifications for the Nash surfaces and the complex algebraic curves. We also address the minimal surfaces with finite total curvature.
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