{"title":"加权流形的正加权质量定理的非自旋方法","authors":"Jianchun Chu, Jintian Zhu","doi":"10.1007/s12220-024-01725-3","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we investigate the weighted mass for weighted manifolds. By establishing a version of density theorem and generalizing Geroch conjecture in the setting of <i>P</i>-scalar curvature, we are able to prove the positive weighted mass theorem for weighted manifolds, which generalizes the result of Baldauf–Ozuch (Commun Math Phys 394(3):1153–1172, 2022) to non-spin manifolds.</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":"224 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Non-spin Method to the Positive Weighted Mass Theorem for Weighted Manifolds\",\"authors\":\"Jianchun Chu, Jintian Zhu\",\"doi\":\"10.1007/s12220-024-01725-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we investigate the weighted mass for weighted manifolds. By establishing a version of density theorem and generalizing Geroch conjecture in the setting of <i>P</i>-scalar curvature, we are able to prove the positive weighted mass theorem for weighted manifolds, which generalizes the result of Baldauf–Ozuch (Commun Math Phys 394(3):1153–1172, 2022) to non-spin manifolds.</p>\",\"PeriodicalId\":501200,\"journal\":{\"name\":\"The Journal of Geometric Analysis\",\"volume\":\"224 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-06-27\",\"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/s12220-024-01725-3\",\"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/s12220-024-01725-3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Non-spin Method to the Positive Weighted Mass Theorem for Weighted Manifolds
In this paper, we investigate the weighted mass for weighted manifolds. By establishing a version of density theorem and generalizing Geroch conjecture in the setting of P-scalar curvature, we are able to prove the positive weighted mass theorem for weighted manifolds, which generalizes the result of Baldauf–Ozuch (Commun Math Phys 394(3):1153–1172, 2022) to non-spin manifolds.
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