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arXiv · 2609.04631

The pinching constant for closed minimal submanifolds of high codimension in the sphere

Hongwei Xu·Entao Zhao
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Abstract

Let $M^n$ be a closed minimal submanifold in the unit sphere $\mathbb{S}^{n+q}$ with $n\geqslant 3$ and $q\geqslant 2$. Let $S$ be the squared length of its second fundamental form and $S_{\max}=\max_{p\in M}S(p)$. We prove that if $M$ is not totally geodesic, then \[ S_{\max}>\frac{2n}{3}+\frac{n-2}{182}. \]

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Hongwei Xu, Entao Zhao. 2026-09-04. The pinching constant for closed minimal submanifolds of high codimension in the sphere. https://arxiv.org/abs/2609.04631

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