Closed hypersurfaces with prescribed Weingarten curvature in Riemannian manifolds

被引：11

作者：

Li, Qi-Rui ^{[1
]}

Sheng, Weimin ^{[1
]}

机构：

[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2013年 / 48卷 / 1-2期

关键词：

SHAPED COMPACT HYPERSURFACES; MEAN-CURVATURE; SPACE; EQUATIONS;

D O I：

10.1007/s00526-012-0540-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider the problem of finding closed hypersurfaces with prescribed Weingarten curvature in a large class of Riemannian manifolds. Under some sufficient conditions, we obtain an existence result by establishing a priori estimates and standard degree theory for the admissible solutions to the prescribed curvature equation. We mainly show that the primary technique developed in Urbas, Wang and the second author's work in 2004 is flexible enough to be used in more general ambient geometry.

引用

页码：41 / 66

页数：26

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