On rigidity of hypersurfaces with constant curvature functions in warped product manifolds

被引：10

作者：

Wu, Jie ^{[1
,2
]}

Xia, Chao ^{[3
]}

机构：

[1] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Peoples R China

[2] Univ Freiburg, Math Inst, D-79104 Freiburg, Germany

[3] Max Planck Inst Math Nat Wissensch, D-04103 Leipzig, Germany

来源：

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2014年 / 46卷 / 01期

基金：

欧洲研究理事会;

关键词：

Constant mean curvature; Rigidity; Warped product manifold; Gauss-Bonnet curvature; MEAN-CURVATURE; SURFACES; OPERATOR;

D O I：

10.1007/s10455-013-9405-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we first investigate several rigidity problems for hypersurfaces in the warped product manifolds with constant linear combinations of higher order mean curvatures as well as "weighted" mean curvatures, which extend the work (Brendle in Publ Math Inst Hautes A parts per thousand tudes Sci 117:247-269, 2013; Brendle and Eichmair in J Differ Geom 94(94):387-407, 2013; Montiel in Indiana Univ Math J 48:711-748, 1999) considering constant mean curvature functions. Secondly, we obtain the rigidity results for hypersurfaces in the space forms with constant linear combinations of intrinsic Gauss-Bonnet curvatures . To achieve this, we develop some new kind of Newton-Maclaurin type inequalities on which may have independent interest.

引用

页码：1 / 22

页数：22

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