An application of maximum principle to space-like hypersurfaces with constant mean curvature in anti-de Sitter space

被引：0
作者：
Changxiong Nie
机构：
[1] Hubei University,Faculty of Mathematics and Computer Sciences
来源：
Monatshefte für Mathematik | 2012年 / 168卷
关键词：
Complete; Space-like; Constant mean curvature; Primary 53A30; Secondary 53C50;
D O I：
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摘要：
In this paper, we study complete hypersurfaces with constant mean curvature in anti-de Sitter space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H^{n+1}_1(-1)}$$\end{document}. we prove that if a complete space-like hypersurface with constant mean curvature \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${x:\mathbf M\rightarrow H^{n+1}_1(-1) }$$\end{document} has two distinct principal curvatures λ, μ, and inf|λ − μ| > 0, then x is the standard embedding \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${ H^{m} (-\frac{1}{r^2})\times H^{n-m} ( -\frac{1}{1 - r^2} )}$$\end{document} in anti-de Sitter space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${ H^{n+1}_1 (-1) }$$\end{document}.
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页码：65 / 73
页数：8
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共 14 条
[1]  
Calabi E.(1970)Examples of Bernstein problems for nonlinear equations Proc. Symp. Pure Math. 15 223-230
[2]  
Cheng S.Y.(1976)Maximal space-like hypersurfaces in the Lorentz–Minkowski space Ann. Math. 104 407-419
[3]  
Yau S.T.(2007)A new characterization of hyperbolic cylinder in anti-de Sitter space J. Math. Anal. Appl. 329 408-414
[4]  
Cao L.(1998)A Liouville-type theorem for complete Riemannian manifolds Bull. Korean Math. Soc. 35 301-309
[5]  
Wei G.(1980)Liouville theorems for harmonic maps Proc. Symp. Pure Math. 36 147-151
[6]  
Choi S.M.(1988)Maximal space-like submanifolds of a pseudo-Riemannian space form of constant curvature Mich. Math. J. 35 345-352
[7]  
Kwon J.-H.(1984)On maximal space-like hypersurfaces in a Lorentzian manifolds Nagoya Math. J. 95 117-124
[8]  
Suh Y.J.(2010)On complete space-like hypersurfaces with constant m-th mean curvature in an anti-de Sitter space Internat. J. Math. 21 551-569
[9]  
Cheng S.Y.(2010)On complete space-like hypersurfaces with two distinct principal curvatures in Lorentz–Minkowski space J. Geom. Phys. 60 43-52
[10]  
Ishihara T.(2009)On hypersurfaces with two distinct principal curvatures in a unit sphere Diff. Geom. Appl. 27 623-634
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