arxiv: 1102.4800 · v1 · pith:7IBYSQCZnew · submitted 2011-02-23 · 🧮 math.DG

An varepsilon-regularity Theorem For The Mean Curvature Flow

Xiaoli Han , Jun Sun This is my paper

classification 🧮 math.DG

keywords curvatureflowmeanpointregularitysmalltheoremapplication

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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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An varepsilon-regularity Theorem For The Mean Curvature Flow

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