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arXiv · 1102.4800

An $\varepsilon$-regularity Theorem For The Mean Curvature Flow

Xiaoli Han·Jun Sun
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Abstract

In this paper, we will derive a small energy regularity theorem for the mean curvature flow of arbitrary dimension and codimension. It says that if the parabolic integral of $|A|^2$ around a point in space-time is small, then the mean curvature flow cannot develop singularity at this point. As an application, we can prove that the 2-dimensional Hausdorff measure of the singular set of the mean curvature flow from a surface to a Riemannian manifold must be zero.

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Xiaoli Han, Jun Sun. 2011-02-23. An $\varepsilon$-regularity Theorem For The Mean Curvature Flow. https://doi.org/10.1016/j.geomphys.2012.07.009

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