A Curvature Gap for Minimal Submanifolds in Spheres

Fagui Li; Yuhang Zhao

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arXiv · 2608.16095

A Curvature Gap for Minimal Submanifolds in Spheres

Fagui Li·Yuhang Zhao

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Abstract

Let $F:M^n\to\Sn^{n+q}(1)$ be a closed minimal immersion in the unit sphere, with $n\ge3$, $q\ge2$. Let $S$ be the squared length of its second fundamental form. We prove that if $M$ is not totally geodesic, then $$ \max_M S> \frac{n(288\sqrt6\,n-288)}{(288\sqrt6+192)n-137} >\frac{2n}{3}+\frac{31-9\sqrt6}{75}(n-2). $$

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Fagui Li, Yuhang Zhao. 2026-08-17. A Curvature Gap for Minimal Submanifolds in Spheres. https://arxiv.org/abs/2608.16095

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