On Chern's problem for rigidity of minimal hypersurfaces in the spheres

被引：45

作者：

Ding, Qi ^{[1
]}

Xin, Y. L. ^{[1
]}

机构：

[1] Fudan Univ, Inst Math, Shanghai 200433, Peoples R China

来源：

ADVANCES IN MATHEMATICS | 2011年 / 227卷 / 01期

关键词：

Minimal hypersurface; Pinching problem; Clifford minimal hypersurface; Intrinsic rigidity; SCALAR CURVATURE;

D O I：

10.1016/j.aim.2011.01.018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a compact minimal hypersurface M in Sn+1 with the squared length of the second fundamental form S we confirm that there exists a positive constant delta(n) depending only on a, such that if n <= S <= n + delta(n), then S equivalent to n, i.e., M is a Clifford minimal hypersurface, in particular, when n >= 6, the pinching constant delta(n) = n/23. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：131 / 145

页数：15

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