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

作　　者：Li Lei Hongwei Xu Zhiyuan Xu 

机构地区：[1]Center of Mathematical Sciences,Zhejiang University,Hangzhou 310027,China [2]Department of Mathematics,Hangzhou Normal University,Hangzhou 310036,China

出　　处：《Science China Mathematics》2021年第7期1493-1504,共12页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11531012);China Postdoctoral Science Foundation(Grant No.BX20180274);Natural Science Foundation of Zhejiang Province(Grant No.LY20A010024)。

摘　　要：Let M be a compact hypersurface with constant mean curvature in 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 constantγ(n)depending only on n such that if|H|≤γ(n)andβ(n,H)≤S≤β(n,H)+n/18,then S≡β(n,H)and M is a Clifford torus.Here,β(n,H)=n+n^(3)/2(n-1)H^(2)+n(n-2)/2(n-1)(1/2)n^(2)H^(4)+4(n-1)H^(2).

关 键 词：generalized Chern conjecture hypersurfaces with constant mean curvature rigidity theorem scalar curvature the second fundamental form 

分 类 号：O186.11[理学—数学]