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A Curvature Gap for Minimal Submanifolds in Spheres
Abstract
Let F:Mn→Snn+q(1) be a closed minimal immersion in the unit sphere, with n≥3, q≥2. Let S be the squared length of its second fundamental form. We prove that if M is not totally geodesic, then maxM S> (n(288√6 n−288))/((288√6+192)n−137) >2n/3+(31−9√6)/75(n−2).
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BibTeX
@misc{li2026curvature,
title = {{A Curvature Gap for Minimal Submanifolds in Spheres}},
author = {Fagui Li and Yuhang Zhao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.16095},
eprint = {2608.16095},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.16095},
}
RIS
TY - UNPB
TI - A Curvature Gap for Minimal Submanifolds in Spheres
AU - Fagui Li
AU - Yuhang Zhao
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2608.16095
UR - https://arxiv.org/abs/2608.16095
AB - Let F:M^n→Sn^n+q(1) be a closed minimal immersion in the unit sphere, with n≥3, q≥2. Let S be the squared length of its second fundamental form. We prove that if M is not totally geodesic, then max_M S> (n(288√6 n−288))/((288√6+192)n−137) >2n/3+(31−9√6)/75(n−2).
ER -