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Tensorial pinching by deforming curvature cones in higher codimension mean curvature flow
Abstract
We develop a pinching method for mean curvature flow in higher codimension. Motivated by pinching constructions for Ricci flow, the method uses a nonlinear deformation of the second fundamental form. We introduce two tensorial curvature conditions for closed immersions in Euclidean space which extend beyond the scope of classical scalar pinching results. In dimensions at least ten, we apply the method to prove convergence to a round point under the first condition and a canonical neighborhood theorem under the second.
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BibTeX
@misc{chow2026tensorial,
title = {{Tensorial pinching by deforming curvature cones in higher codimension mean curvature flow}},
author = {Tsz-Kiu Aaron Chow},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25610},
eprint = {2610.25610},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25610},
}
RIS
TY - UNPB
TI - Tensorial pinching by deforming curvature cones in higher codimension mean curvature flow
AU - Tsz-Kiu Aaron Chow
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.25610
UR - https://arxiv.org/abs/2610.25610
AB - We develop a pinching method for mean curvature flow in higher codimension. Motivated by pinching constructions for Ricci flow, the method uses a nonlinear deformation of the second fundamental form. We introduce two tensorial curvature conditions for closed immersions in Euclidean space which extend beyond the scope of classical scalar pinching results. In dimensions at least ten, we apply the method to prove convergence to a round point under the first condition and a canonical neighborhood theorem under the second.
ER -