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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Hypersurfaces in a sphere
with constant mean curvature

Author: Zhong Hua Hou
Journal: Proc. Amer. Math. Soc. 125 (1997), 1193-1196
MSC (1991): Primary 53C42, 53A10
MathSciNet review: 1363169
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Abstract: Let $M^n$ be a closed hypersurface of constant mean curvature immersed in the unit sphere $S^{n+1}$. Denote by $S$ the square of the length of its second fundamental form. If $S<2\sqrt {n-1}$, $M$ is a small hypersphere in $S^{n+1}$. We also characterize all $M^n$ with $S=2\sqrt {n-1}$.

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Zhong Hua Hou
Affiliation: Department of Mathematics, Tokyo Institute of Technology, Japan; Department of Applied Mathematics, Dalian University of Technology, People’s Republic of China

Received by editor(s): July 27, 1995
Communicated by: Peter Li
Article copyright: © Copyright 1997 American Mathematical Society