Starshaped compact hypersurfaces with prescribed Weingarten curvature in warped product manifolds

被引：23

作者：

Chen, Daguang ^{[1
]}

Li, Haizhong ^{[1
]}

Wang, Zhizhang ^{[2
]}

机构：

[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2018年 / 57卷 / 02期

关键词：

2ND-ORDER ELLIPTIC-EQUATIONS; DIRICHLET PROBLEM;

D O I：

10.1007/s00526-018-1314-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a compact Riemannian manifold M, we consider awarped productmanifold (M) over bar = Ix(h)M, where I is an open interval in R. For a positive function psi defined on (M) over bar, wegeneralize the arguments in Guan et al. (Commun. Pure Appl. Math. 68(8):1287-1325, 2015) and Ren andWang (On the curvature estimates for Hessian equations, 2016. arXiv: 1602.06535), to obtain the curvature estimates for Hessian equations sigma(k)(kappa) =psi(V, v(V)). We also obtain some existence results for the starshaped compact hypersurface Sigma satisfying the above equation with various assumptions.

引用

页数：26

共 48 条

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