On the compactness of constant mean curvature hypersurfaces with finite total curvature

被引：0
|
作者：
Manfredo P. do Carmo
Leung-Fu Cheung
Walcy Santos
机构：
[1] I.M.P.A.,
[2] Estrada Dona Castorina 110,undefined
[3] Jardim Botânico,undefined
[4] 22460-320 Rio de Janeiro,undefined
[5] Brazil,undefined
[6] Department of Applied Mathematics,undefined
[7] The Hong Kong Polytechnic,undefined
[8] University,undefined
[9] Hung Hom,undefined
[10] Kowloon,undefined
[11] Hong Kong,undefined
[12] Departamento de Matemática,undefined
[13] Universidade Federal do,undefined
[14] Rio de Janeiro,undefined
[15] Caixa Postal 68530,undefined
[16] 21945-970 Rio de Janeiro,undefined
[17] Brazil,undefined
来源：
Archiv der Mathematik | 1999年 / 73卷
关键词：
Space Form; Curvature Vector; Total Curvature; Curvature Hypersurface; Finite Total Curvature;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this work we consider a complete submanifold M with parallel mean curvature vector h immersed in a space form of constant sectional curvature \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $c\leq 0$\end{document}. If M has finite total curvature and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $|H|^2>-c$\end{document}, we prove that M must be compact.
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页码：216 / 222
页数：6
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