{"title":"Rigidity of Free Boundary Minimal Disks in Mean Convex Three-Manifolds","authors":"Rondinelle Batista, Barnabé Lima, João Silva","doi":"10.1007/s12220-024-01727-1","DOIUrl":null,"url":null,"abstract":"<p>The purpose of this article is to study rigidity of free boundary minimal two-disks that locally maximize the modified Hawking mass on a Riemannian three-manifold with a positive lower bound on its scalar curvature and mean convex boundary. Assuming the strict stability of <span>\\(\\Sigma \\)</span>, we prove that a neighborhood of it in <i>M</i> is isometric to one of the half de Sitter–Schwarzschild space.</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":"22 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-28","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/s12220-024-01727-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
The purpose of this article is to study rigidity of free boundary minimal two-disks that locally maximize the modified Hawking mass on a Riemannian three-manifold with a positive lower bound on its scalar curvature and mean convex boundary. Assuming the strict stability of \(\Sigma \), we prove that a neighborhood of it in M is isometric to one of the half de Sitter–Schwarzschild space.
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