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arXiv · 1012.1073

Some results on Chern's problem

Qi Ding·Y. L. Xin
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Abstract

For a compact minimal hypersurface $M$ in $S^{n+1}$ with the squared length of the second fundamental form $S$ we confirm that there exists a positive constant $\de(n)$ depending only on $n,$ such that if $n\leq S\leq n +\delta(n)$, then $S\equiv n$, i.e., $M$ is a Clifford minimal hypersurface, in particular, when $n\ge 6,$ the pinching constant $\de(n)=\f{n}{23}.$

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Qi Ding, Y. L. Xin. 2010-12-06. Some results on Chern's problem. https://arxiv.org/abs/1012.1073

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