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arXiv · 2104.14057

Chern conjecture on minimal hypersurfaces

Qing-Ming Cheng·Guoxin Wei·Takuya Yamashiro
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Abstract

In this paper, we study $n$-dimensional complete minimal hypersurfaces in a unit sphere. We prove that an $n$-dimensional complete minimal hypersurface with constant scalar curvature in a unit sphere with $f_3$ constant is isometric to the totally geodesic sphere or the Clifford torus if $S\leq 1.8252 n-0.712898$, where $S$ denotes the squared norm of the second fundamental form of this hypersurface.

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Qing-Ming Cheng, Guoxin Wei, Takuya Yamashiro. 2021-04-29. Chern conjecture on minimal hypersurfaces. https://arxiv.org/abs/2104.14057

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