The pinching constant of minimal hypersurfaces in the unit spheres
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Abstract:
In this paper, we prove that if $M^n$ ($n\leq 8$) 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 $M$.References
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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
- 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
- © Copyright 2009 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 138 (2010), 1833-1841
- MSC (2000): Primary 53C40
- DOI: https://doi.org/10.1090/S0002-9939-09-10251-4
- MathSciNet review: 2587468