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arXiv · 1805.11808

Cylindrical Estimates for High Codimension Mean Curvature Flow

Huy The Nguyen
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Abstract

We study high codimension mean curvature flow of a submanifold $\mathcal{M}^n$ of dimension $n$ in Euclidean space $\mathbb{R}^{n+k}$ subject to the quadratic curvature condition $ |A|^{2}\leq c_n |H|^{2}, c _n = \min\{ \frac{4}{3n} , \frac{1}{n-2}\}$. This condition extends the notion of two-convexity for hypersurfaces to high codimension submanifolds. We analyse singularity formation in the mean curvature flow of high codimension by directly proving a pointwise gradient estimate. We then show that near a singularity the surface is quantitatively cylindrical.

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Huy The Nguyen. 2018-05-30. Cylindrical Estimates for High Codimension Mean Curvature Flow. https://arxiv.org/abs/1805.11808

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