{"title":"小曲率集中流形上的差距定理","authors":"Pak-Yeung Chan, Man-Chun Lee","doi":"10.1007/s00209-024-03570-0","DOIUrl":null,"url":null,"abstract":"<p>In this work, we show that complete non-compact manifolds with non-negative Ricci curvature, Euclidean volume growth and sufficiently small curvature concentration are necessarily flat Euclidean space.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Gap Theorem on manifolds with small curvature concentration\",\"authors\":\"Pak-Yeung Chan, Man-Chun Lee\",\"doi\":\"10.1007/s00209-024-03570-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this work, we show that complete non-compact manifolds with non-negative Ricci curvature, Euclidean volume growth and sufficiently small curvature concentration are necessarily flat Euclidean space.</p>\",\"PeriodicalId\":18278,\"journal\":{\"name\":\"Mathematische Zeitschrift\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-07-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematische Zeitschrift\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00209-024-03570-0\",\"RegionNum\":3,\"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":"Mathematische Zeitschrift","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00209-024-03570-0","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Gap Theorem on manifolds with small curvature concentration
In this work, we show that complete non-compact manifolds with non-negative Ricci curvature, Euclidean volume growth and sufficiently small curvature concentration are necessarily flat Euclidean space.
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