On the generalized Chern conjecture for hypersurfaces with constant mean curvature in a sphere

被引：4
|
作者：
Lei, Li [1 ]
Xu, Hongwei [1 ]
Xu, Zhiyuan [2 ]
机构：
[1] Zhejiang Univ, Ctr Math Sci, Hangzhou 310027, Peoples R China
[2] Hangzhou Normal Univ, Dept Math, Hangzhou 310036, Peoples R China
来源：
SCIENCE CHINA-MATHEMATICS | 2021年 / 64卷 / 07期
基金：
中国国家自然科学基金; 中国博士后科学基金;
关键词：
generalized Chern conjecture; hypersurfaces with constant mean curvature; rigidity theorem; scalar curvature; the second fundamental form;
D O I：
10.1007/s11425-020-1841-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let M be a compact hypersurface with constant mean curvature in Sn+1. Denote by H and S the mean curvature and the squared norm of the second fundamental form of M, respectively. We verify that there exists a positive constant gamma(n) depending only on n such that if jHj 6 gamma(n) and fi(n;H) 6 S 6 fi(n;H) + n 18, then S beta (n;H) and M is a Clifford torus. Here, fi (n;H) = n + n3 2(n H2 + n(n 2(n v n2H4 + 4(n 1)H2
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页码：1493 / 1504
页数：12
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