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

被引：5

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：

中国博士后科学基金; 中国国家自然科学基金;

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

引用

页码：1493 / 1504

页数：12

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