A NEW PINCHING THEOREM FOR CLOSED HYPERSURFACES WITH CONSTANT MEAN CURVATURE IN Sn+1

被引：0

作者：

Xu, Hong-Wei ^{[1
]}

Tian, Ling ^{[1
]}

机构：

[1] Zhejiang Univ, Ctr Math Sci, Hangzhou 310027, Zhejiang, Peoples R China

来源：

ASIAN JOURNAL OF MATHEMATICS | 2011年 / 15卷 / 04期

关键词：

Closed hypersurface; Pinching phenomenon; Mean curvature; Scalar curvature; Second fundamental form; MINIMAL HYPERSURFACES; SCALAR CURVATURE; UNIT-SPHERE; RIGIDITY THEOREM; CLIFFORD TORUS; SUBMANIFOLDS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the generalized Chern conjecture, and prove that if M is a closed hypersurface in Sn+1 with constant scalar curvature and constant mean curvature, then there exists an explicit positive constant C(n) depending only on n such that if vertical bar H vertical bar < C( n) and S > beta(n, H), then S > beta(n, H) + 3n/7, where beta (n, H) = n + n(3)H(2)/2(n-1) + n(n-2)/2(n-1)root n(2)H(4) + 4(n - 1)H-2.

引用

页码：611 / 630

页数：20

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