双曲空间中的曲率测度问题

IF 3.1 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics Pub Date : 2023-09-07 DOI:10.1002/cpa.22160

Fengrui Yang

{"title":"双曲空间中的曲率测度问题","authors":"Fengrui Yang","doi":"10.1002/cpa.22160","DOIUrl":null,"url":null,"abstract":"The problem of the prescribed curvature measure is one of the important problems in differential geometry and nonlinear partial differential equations. In this paper, we consider the prescribed curvature measure problem in the hyperbolic space. We obtain the existence of star-shaped k-convex bodies with prescribed (n-k)-th curvature measures <math>\n <semantics>\n <mrow>\n <mo>(</mo>\n <mi>k</mi>\n <mo><</mo>\n <mi>n</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$(k<n)$</annotation>\n </semantics></math> by establishing crucial C2 regularity estimates for solutions to the corresponding fully nonlinear PDE in the hyperbolic space.","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.1000,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Prescribed curvature measure problem in hyperbolic space\",\"authors\":\"Fengrui Yang\",\"doi\":\"10.1002/cpa.22160\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The problem of the prescribed curvature measure is one of the important problems in differential geometry and nonlinear partial differential equations. In this paper, we consider the prescribed curvature measure problem in the hyperbolic space. We obtain the existence of star-shaped k-convex bodies with prescribed (n-k)-th curvature measures <math>\\n <semantics>\\n <mrow>\\n <mo>(</mo>\\n <mi>k</mi>\\n <mo><</mo>\\n <mi>n</mi>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$(k<n)$</annotation>\\n </semantics></math> by establishing crucial C2 regularity estimates for solutions to the corresponding fully nonlinear PDE in the hyperbolic space.\",\"PeriodicalId\":10601,\"journal\":{\"name\":\"Communications on Pure and Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.1000,\"publicationDate\":\"2023-09-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications on Pure and Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/cpa.22160\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications on Pure and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/cpa.22160","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 4

摘要

曲率测度问题是微分几何和非线性偏微分方程中的一个重要问题。本文考虑双曲空间中的曲率测度问题。通过对双曲空间中相应的全非线性PDE的解建立关键的C2正则性估计，我们获得了具有规定曲率测度的星形k凸体的存在性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Prescribed curvature measure problem in hyperbolic space

The problem of the prescribed curvature measure is one of the important problems in differential geometry and nonlinear partial differential equations. In this paper, we consider the prescribed curvature measure problem in the hyperbolic space. We obtain the existence of star-shaped k-convex bodies with prescribed (n-k)-th curvature measures $(k < n)$ by establishing crucial C² regularity estimates for solutions to the corresponding fully nonlinear PDE in the hyperbolic space.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Communications on Pure and Applied Mathematics 数学-数学

CiteScore

6.70

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.