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arXiv · 1712.01175

On Chern's conjecture for minimal hypersurfaces in spheres

Li Lei·Hongwei Xu·Zhiyuan Xu
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Abstract

Using a new estimate for the Peng-Terng invariant and the multiple-parameter method, we verify a rigidity theorem on the stronger version of Chern Conjecture for minimal hypersurfaces in spheres. More precisely, we prove that if $M$ is a compact minimal hypersurface in $\mathbb{S}^{n+1}$ whose squared length of the second fundamental form satisfies $0\leq S-n\leq\frac{n}{18}$, then $S\equiv n$ and $M$ is a Clifford torus.

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Li Lei, Hongwei Xu, Zhiyuan Xu. 2017-12-04. On Chern's conjecture for minimal hypersurfaces in spheres. https://arxiv.org/abs/1712.01175

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