{"title":"Hilbert空间中几乎最小化可直G链的部分正则性","authors":"Thierry de Pauw, Roger Züst","doi":"10.1353/ajm.2019.0044","DOIUrl":null,"url":null,"abstract":"Abstract:We adapt to an infinite dimensional ambient space E. R. Reifenberg's epiperimetric inequality and a quantitative version of D. Preiss' second moments computations to establish that the set of regular points of an almost mass minimizing rectifiable $G$ chain in $\\ell_2$ is dense in its support, whenever the group $G$ of coefficients is so that $\\{\\|g\\|:g\\in G\\}$ is discrete.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2019-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1353/ajm.2019.0044","citationCount":"0","resultStr":"{\"title\":\"Partial regularity of almost minimizing rectifiable G chains in Hilbert space\",\"authors\":\"Thierry de Pauw, Roger Züst\",\"doi\":\"10.1353/ajm.2019.0044\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract:We adapt to an infinite dimensional ambient space E. R. Reifenberg's epiperimetric inequality and a quantitative version of D. Preiss' second moments computations to establish that the set of regular points of an almost mass minimizing rectifiable $G$ chain in $\\\\ell_2$ is dense in its support, whenever the group $G$ of coefficients is so that $\\\\{\\\\|g\\\\|:g\\\\in G\\\\}$ is discrete.\",\"PeriodicalId\":7453,\"journal\":{\"name\":\"American Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2019-11-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1353/ajm.2019.0044\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"American Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1353/ajm.2019.0044\",\"RegionNum\":1,\"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":"American Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1353/ajm.2019.0044","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Partial regularity of almost minimizing rectifiable G chains in Hilbert space
Abstract:We adapt to an infinite dimensional ambient space E. R. Reifenberg's epiperimetric inequality and a quantitative version of D. Preiss' second moments computations to establish that the set of regular points of an almost mass minimizing rectifiable $G$ chain in $\ell_2$ is dense in its support, whenever the group $G$ of coefficients is so that $\{\|g\|:g\in G\}$ is discrete.
期刊介绍：
The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.
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