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

作　　者：Yi Bing SHEN Xiao Hua ZHU 

机构地区：[1]Department of Mathematics Zhejiang University, Hangzhou 310028, P. R. China [2]School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》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.

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.

关 键 词：Constant mean curvature Strong stability L^p-norm curvature 

分 类 号：O187.1[理学—数学]