{"title":"The Dirichlet problem for a class of curvature equations in Minkowski space","authors":"Mengru Guo, Heming Jiao","doi":"arxiv-2409.03308","DOIUrl":null,"url":null,"abstract":"In this paper, we study the Dirichlet problem for a class of prescribed\ncurvature equations in Minkowski space. We prove the existence of smooth\nspacelike hypersurfaces with a class of prescribed curvature and general\nboundary data based on establishing the \\emph{a priori} $C^2$ estimates.","PeriodicalId":501113,"journal":{"name":"arXiv - MATH - Differential Geometry","volume":"14 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Differential Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.03308","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
In this paper, we study the Dirichlet problem for a class of prescribed
curvature equations in Minkowski space. We prove the existence of smooth
spacelike hypersurfaces with a class of prescribed curvature and general
boundary data based on establishing the \emph{a priori} $C^2$ estimates.
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