{"title":"Sharp bottom spectrum and scalar curvature rigidity","authors":"Jinmin Wang, Bo Zhu","doi":"arxiv-2408.08245","DOIUrl":null,"url":null,"abstract":"We prove a sharp upper bound for the bottom spectrum of Laplacian on\ngeometrically contractible manifolds with scalar curvature lower bound, and\ncharacterize the distribution of scalar curvature when equality holds.\nMoreover, we prove a scalar curvature rigidity theorem if the manifold is the\nuniversal cover of a closed hyperbolic manifold.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Operator Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.08245","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We prove a sharp upper bound for the bottom spectrum of Laplacian on
geometrically contractible manifolds with scalar curvature lower bound, and
characterize the distribution of scalar curvature when equality holds.
Moreover, we prove a scalar curvature rigidity theorem if the manifold is the
universal cover of a closed hyperbolic manifold.