{"title":"流形上正对称张量场的迈克尔-西蒙-索博列夫不等式","authors":"Yuting Wu, Chengyang Yi, Yu Zheng","doi":"arxiv-2409.08011","DOIUrl":null,"url":null,"abstract":"We prove the Michael-Simon-Sobolev inequality for smooth symmetric uniformly\npositive definite (0, 2)-tensor fields on compact submanifolds with or without\nboundary in Riemannian manifolds with nonnegative sectional curvature by the\nAlexandrov-Bakelman-Pucci (ABP) method. It should be a generalization of S.\nBrendle in [2].","PeriodicalId":501113,"journal":{"name":"arXiv - MATH - Differential Geometry","volume":"7 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Michael-Simon-Sobolev inequality on manifolds for positive symmetric tensor fields\",\"authors\":\"Yuting Wu, Chengyang Yi, Yu Zheng\",\"doi\":\"arxiv-2409.08011\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove the Michael-Simon-Sobolev inequality for smooth symmetric uniformly\\npositive definite (0, 2)-tensor fields on compact submanifolds with or without\\nboundary in Riemannian manifolds with nonnegative sectional curvature by the\\nAlexandrov-Bakelman-Pucci (ABP) method. It should be a generalization of S.\\nBrendle in [2].\",\"PeriodicalId\":501113,\"journal\":{\"name\":\"arXiv - MATH - Differential Geometry\",\"volume\":\"7 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Differential Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.08011\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Differential Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.08011","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Michael-Simon-Sobolev inequality on manifolds for positive symmetric tensor fields
We prove the Michael-Simon-Sobolev inequality for smooth symmetric uniformly
positive definite (0, 2)-tensor fields on compact submanifolds with or without
boundary in Riemannian manifolds with nonnegative sectional curvature by the
Alexandrov-Bakelman-Pucci (ABP) method. It should be a generalization of S.
Brendle in [2].
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