The pinching constant of minimal hypersurfaces in the unit spheres

Zhang, Qin

doi:10.1090/S0002-9939-09-10251-4

The pinching constant of minimal hypersurfaces in the unit spheres
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Proc. Amer. Math. Soc. 138 (2010), 1833-1841 Request permission

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 $M$.

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