{"title":"一些质量容量不平等的影响","authors":"Pengzi Miao","doi":"10.1007/s12220-024-01686-7","DOIUrl":null,"url":null,"abstract":"<p>Applying a family of mass-capacity related inequalities proved in Miao (Peking Math J 2023, https://doi.org/10.1007/s42543-023-00071-7), we obtain sufficient conditions that imply the nonnegativity as well as positive lower bounds of the mass, on a class of manifolds with nonnegative scalar curvature, with or without a singularity.</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":"52 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Implications of Some Mass-Capacity Inequalities\",\"authors\":\"Pengzi Miao\",\"doi\":\"10.1007/s12220-024-01686-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Applying a family of mass-capacity related inequalities proved in Miao (Peking Math J 2023, https://doi.org/10.1007/s42543-023-00071-7), we obtain sufficient conditions that imply the nonnegativity as well as positive lower bounds of the mass, on a class of manifolds with nonnegative scalar curvature, with or without a singularity.</p>\",\"PeriodicalId\":501200,\"journal\":{\"name\":\"The Journal of Geometric Analysis\",\"volume\":\"52 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-05-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Journal of Geometric Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s12220-024-01686-7\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Journal of Geometric Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s12220-024-01686-7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
应用苗（Peking Math J 2023, https://doi.org/10.1007/s42543-023-00071-7）中证明的一系列与质量容量相关的不等式，我们得到了充分条件，意味着在一类具有非负标量曲率的流形上，无论是否存在奇点，质量的非负下界和正下界。
Applying a family of mass-capacity related inequalities proved in Miao (Peking Math J 2023, https://doi.org/10.1007/s42543-023-00071-7), we obtain sufficient conditions that imply the nonnegativity as well as positive lower bounds of the mass, on a class of manifolds with nonnegative scalar curvature, with or without a singularity.
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