A canonical neighborhood theorem for the mean curvature flow in higher codimension

Keaton Naff

A canonical neighborhood theorem for the mean curvature flow in higher codimension

Differential Geometry 2022-07-14 v3

Authors: Keaton Naff

Abstract

In dimensions $n \geq 5$ , we prove a canonical neighborhood theorem for the mean curvature flow of compact $n$ -dimensional submanifolds in $\mathbb{R}^N$ satisfying a pinching condition $|A|^2 < c|H|^2$ for $c = \min \{ \frac{3(n+1)}{2n(n+2)},\frac{1}{n-2}\}.$

Keywords

mean curvature flow canonical neighborhood theorem higher codimension pinching condition submanifolds

Cite

@article{arxiv.2004.08060,
  title  = {A canonical neighborhood theorem for the mean curvature flow in higher codimension},
  author = {Keaton Naff},
  journal= {arXiv preprint arXiv:2004.08060},
  year   = {2022}
}

Comments

final version, to appear in IMRN

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