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December 2011 A New Pinching Theorem for Closed Hypersurfaces with Constant Mean Curvature in $S^{n+1}$
Hong-Wei Xu, Ling Tian
Asian J. Math. 15(4): 611-630 (December 2011).

Abstract

We investigate the generalized Chern conjecture, and prove that if $M$ is a closed hypersurface in $S^{n+1}$ with constant scalar curvature and constant mean curvature, then there exists an explicit positive constant $C(n)$ depending only on $n$ such that if $|H| < C(n)$ and $S > \beta (n,H)$, then $S > \beta (n,H) + \frac{3n}{7}$, where $\beta(n,H) = n + \frac{n^3 H^2}{2(n−1)} + \frac{n(n−2)}{2(n−1)} \sqrt{n^2 H^4 + 4(n − 1)H^2}$.

Citation

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Hong-Wei Xu. Ling Tian. "A New Pinching Theorem for Closed Hypersurfaces with Constant Mean Curvature in $S^{n+1}$." Asian J. Math. 15 (4) 611 - 630, December 2011.

Information

Published: December 2011
First available in Project Euclid: 12 March 2012

zbMATH: 1243.53104
MathSciNet: MR2853651

Subjects:
Primary: 53C40 , 53C42

Keywords: Closed hypersurface , mean curvature , pinching phenomenon , Scalar curvature , second fundamental form

Rights: Copyright © 2011 International Press of Boston

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Vol.15 • No. 4 • December 2011
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