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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The pinching constant of minimal hypersurfaces in the unit spheres


Author: Qin Zhang
Journal: Proc. Amer. Math. Soc. 138 (2010), 1833-1841
MSC (2000): Primary 53C40
Published electronically: December 31, 2009
MathSciNet review: 2587468
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Abstract: In this paper, we prove that if $ M^n$ ($ n\leq8$) is a closed minimal hypersurface in a unit sphere $ S^{n+1}(1)$, then there exists a positive constant $ \alpha (n)$ depending only on $ n$ such that if $ n\leq S \leq n+\alpha(n)$, then $ M$ is isometric to a Clifford torus, where $ S$ is the squared norm of the second fundamental form of $ M$.


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Additional Information

Qin Zhang
Affiliation: Institute of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, People’s Republic of China
Email: zhangdiligence@126.com

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10251-4
PII: S 0002-9939(09)10251-4
Keywords: Minimal hypersurface, Clifford torus, second fundamental form
Received by editor(s): June 7, 2009
Received by editor(s) in revised form: August 18, 2009
Published electronically: December 31, 2009
Communicated by: Richard A. Wentworth
Article copyright: © Copyright 2009 American Mathematical Society