{"title":"Curvature estimates for $p$-convex hypersurfaces of prescribed curvature","authors":"Weisong Dong","doi":"10.4171/rmi/1348","DOIUrl":null,"url":null,"abstract":". In this paper, we establish curvature estimates for p -convex hypersurfaces in R n +1 of prescribed curvature with p ≥ n 2 . The existence of a star-shaped hypersurface of prescribed curvature is obtained. We also prove a type of interior C 2 estimates for solutions to the Dirichlet problem of the corresponding equation. Mathematical Subject Classification (2010): 53C42; 53C21; 35J60.","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2021-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista Matematica Iberoamericana","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/rmi/1348","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
. In this paper, we establish curvature estimates for p -convex hypersurfaces in R n +1 of prescribed curvature with p ≥ n 2 . The existence of a star-shaped hypersurface of prescribed curvature is obtained. We also prove a type of interior C 2 estimates for solutions to the Dirichlet problem of the corresponding equation. Mathematical Subject Classification (2010): 53C42; 53C21; 35J60.
期刊介绍：
Revista Matemática Iberoamericana publishes original research articles on all areas of mathematics. Its distinguished Editorial Board selects papers according to the highest standards. Founded in 1985, Revista is a scientific journal of Real Sociedad Matemática Española.
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