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

被引:0
作者
Jie Wu
Chao Xia
机构
[1] University of Science and Technology of China,School of Mathematical Sciences
[2] Albert-Ludwigs-Universität Freiburg,Mathematisches Institut
[3] Max-Planck-Institut für Mathematik in den Naturwissenschaft,undefined
来源
Annals of Global Analysis and Geometry | 2014年 / 46卷
关键词
Constant mean curvature; Rigidity; Warped product manifold; Gauss–Bonnet curvature; Primary 53C24; Secondary 52A20; 53C40;
D O I
暂无
中图分类号
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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 Études 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 Lk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_k$$\end{document}. To achieve this, we develop some new kind of Newton–Maclaurin type inequalities on Lk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_k$$\end{document} which may have independent interest.
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页码:1 / 22
页数:21
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