{"title":"p-凸超曲面规定曲率方程的Dirichlet问题","authors":"Weisong Dong","doi":"10.1007/s00229-023-01522-2","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we study the Dirichlet problem for <i>p</i>-convex hypersurfaces with prescribed curvature. We prove that there exists a graphic hypersurface satisfying the prescribed curvature equation with homogeneous boundary condition. An interior curvature estimate is also obtained.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"18 5-6","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Dirichlet problem for prescribed curvature equations of p-convex hypersurfaces\",\"authors\":\"Weisong Dong\",\"doi\":\"10.1007/s00229-023-01522-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we study the Dirichlet problem for <i>p</i>-convex hypersurfaces with prescribed curvature. We prove that there exists a graphic hypersurface satisfying the prescribed curvature equation with homogeneous boundary condition. An interior curvature estimate is also obtained.</p>\",\"PeriodicalId\":49887,\"journal\":{\"name\":\"Manuscripta Mathematica\",\"volume\":\"18 5-6\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-11-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Manuscripta Mathematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00229-023-01522-2\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Manuscripta Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00229-023-01522-2","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
The Dirichlet problem for prescribed curvature equations of p-convex hypersurfaces
In this paper, we study the Dirichlet problem for p-convex hypersurfaces with prescribed curvature. We prove that there exists a graphic hypersurface satisfying the prescribed curvature equation with homogeneous boundary condition. An interior curvature estimate is also obtained.
期刊介绍：
manuscripta mathematica was founded in 1969 to provide a forum for the rapid communication of advances in mathematical research. Edited by an international board whose members represent a wide spectrum of research interests, manuscripta mathematica is now recognized as a leading source of information on the latest mathematical results.
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