Year: 2026
Type: preprint
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 \[ S_{\max}>\frac{2n}{3}+\frac{n-2}{182}. \]
Source: arXiv (Cornell University)
Authors: Xu, Hongwei, Zhao, Entao
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1615997487, G3559238355, 子流形几何与曲率流的若干研究
OpenAlex ID: W7211878119