An Extension of Hsiung-Minkowski Formulas and Some Applications

被引：18

作者：

Kwong, Kwok-Kun ^{[1
]}

机构：

[1] Natl Cheng Kung Univ, Dept Math, Tainan 701, Taiwan

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2016年 / 26卷 / 01期

关键词：

Hsiung-Minkowski formulas; Alexandrov's theorem; Conformal Killing vector fields; Eigenvalue estimate; MEAN-CURVATURE FUNCTIONS; INTEGRAL FORMULAS; SPACELIKE HYPERSURFACES; SPHERE THEOREM; 1ST EIGENVALUE; UPPER-BOUNDS; MANIFOLDS; SUBMANIFOLDS; LAPLACIAN; OPERATOR;

D O I：

10.1007/s12220-014-9536-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a generalization of Hsiung-Minkowski formulas for closed sub-manifolds in semi-Riemannian manifolds with constant curvature. As a corollary, we obtain volume and area upper bounds for k-convex hypersurfaces in terms of a weighted total k-th mean curvature of the hypersurface. We also obtain some Alexandrov-type results and some eigenvalue estimates for hypersurfaces.

引用

页码：1 / 23

页数：23

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