Hypersurfaces in a sphere with constant mean curvature

Hou, Zhong

doi:10.1090/S0002-9939-97-03668-X

Hypersurfaces in a sphere with constant mean curvature
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by Zhong Hua Hou

Proc. Amer. Math. Soc. 125 (1997), 1193-1196

DOI: https://doi.org/10.1090/S0002-9939-97-03668-X

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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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