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arXiv · 1704.00431

Non-fattening of mean curvature flow at singularities of mean convex type

Or Hershkovits·Brian White
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Abstract

We show that a mean curvature flow starting from a compact, smoothly embedded hypersurface M remains unique past singularities, provided the singularities are of mean convex type, i.e., if around each singular point, the surface moves in one direction. Specifically, the level set flow of M does not fatten if all singularities are of mean convex type. This generalizes the well known fact that the level set flow of a mean convex initial hypersurface M does not fatten. This also provides the first instance where non-fattening is concluded from local information around the singular set.

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Or Hershkovits, Brian White. 2017-04-03. Non-fattening of mean curvature flow at singularities of mean convex type. https://arxiv.org/abs/1704.00431

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