Author

Yu-Hang Zhao

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Preprint Aug 2026

A Curvature Gap for Minimal Submanifolds in Spheres

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 $$ \max_M S>\frac{n(288\sqrt6\,n-288)}{(288\sqrt6+192)n-137}>\frac{2n}{3}+\frac{31-9\sqrt6}{75}(n-2). $$

Fa-Gui Li, Yu-Hang Zhao · 3 citations · ⚡1

Preprint Aug 2026

A Curvature Gap for Minimal Submanifolds in Spheres

Let $F:M^n\to\Sn^{n+q}(1)$ be a closed connected minimal immersion in the unit sphere with second fundamental form $h$, $n\ge3$, $q\ge2$, and $S=|h|^2$. We prove that if $M$ is not totally geodesic, then \[ \max_M S\ge \frac{2n}{3}+\frac{n-2}{6300(39n+8)} \ge\frac{2n}{3}+\frac1{787500}. \]

Fagui Li, Yuhang Zhao · 2 citations · ⚡1