{"title":"On mass-minimizing extensions of Bartnik boundary data","authors":"An,Zhongshan","doi":"10.4310/cag.2023.v31.n6.a2","DOIUrl":null,"url":null,"abstract":"We prove that the space of initial data sets which solve the constraint equations and have fixed Bartnik boundary data is a Banach manifold. Moreover if an initial data set on this constraint manifold is a critical point of the ADM total mass, then it must admit a generalised Killing vector field which is asymptotically proportional to the ADM energy-momentum vector.","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":"422 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Analysis and Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/cag.2023.v31.n6.a2","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
We prove that the space of initial data sets which solve the constraint equations and have fixed Bartnik boundary data is a Banach manifold. Moreover if an initial data set on this constraint manifold is a critical point of the ADM total mass, then it must admit a generalised Killing vector field which is asymptotically proportional to the ADM energy-momentum vector.
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