PreprintarXiv licencearXiv
The pinching constant for closed minimal submanifolds of high codimension in the sphere
Abstract
Let Mn be a closed minimal submanifold in the unit sphere šn+q with ngeqslant 3 and qgeqslant 2. Let S be the squared length of its second fundamental form and Smax=maxpā MS(p). We prove that if M is not totally geodesic, then Smax>2n/3+(nā2)/182.
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BibTeX
@misc{xu2026pinching,
title = {{The pinching constant for closed minimal submanifolds of high codimension in the sphere}},
author = {Hongwei Xu and Entao Zhao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04631},
eprint = {2609.04631},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04631},
}
RIS
TY - UNPB
TI - The pinching constant for closed minimal submanifolds of high codimension in the sphere
AU - Hongwei Xu
AU - Entao Zhao
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.04631
UR - https://arxiv.org/abs/2609.04631
AB - Let M^n be a closed minimal submanifold in the unit sphere š^n+q with ngeqslant 3 and qgeqslant 2. Let S be the squared length of its second fundamental form and S_max=max_pā MS(p). We prove that if M is not totally geodesic, then S_max>2n/3+(nā2)/182.
ER -