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On Complete Hypersurfaces with Constant Mean Curvature and Finite L^p-norm Curvature in R^(n+1)

On Complete Hypersurfaces with Constant Mean Curvature and Finite L^p-norm Curvature in R^(n+1)
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摘要 By using curvature estimates, we prove that a complete non-compact hypersurface M with constant mean curvature and finite L^n-norm curvature in R^1＋1 must be minimal, so that M is a hyperplane if it is strongly stable. This is a generalization of the result on stable complete minimal hypersurfaces of R^n＋1. Moreover, complete strongly stable hypersurfaces with constant mean curvature and finite L^1-norm curvature in R^1＋1 are considered. By using curvature estimates, we prove that a complete non-compact hypersurface M with constant mean curvature and finite L^n-norm curvature in R^1＋1 must be minimal, so that M is a hyperplane if it is strongly stable. This is a generalization of the result on stable complete minimal hypersurfaces of R^n＋1. Moreover, complete strongly stable hypersurfaces with constant mean curvature and finite L^1-norm curvature in R^1＋1 are considered.
作者 Yi Bing SHEN Xiao Hua ZHU
机构地区 Department of Mathematics Zhejiang University School of Mathematical Sciences
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2005年第3期631-642,共12页 数学学报（英文版）
基金 The first author is partially supported by the National Natural Science Foundation of China (No.10271106) The second author is partially supported by the 973-Grant of Mathematics in China and the Huo Y.-D. fund.
关键词 Constant mean curvature Strong stability L^p-norm curvature Constant mean curvature, Strong stability, L^p-norm curvature
分类号 O187.1 [理学—基础数学]
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参考文献14

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Acta Mathematica Sinica,English Series
2005年 第3期

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