Subsequent Singularities in Mean-Convex Mean Curvature Flow

Details Subsequent Singularities in Mean-Convex Mean Curvature Flow Subsequent Singularities in Mean-Convex Mean Curvature Flow

2011-03-08

arxiv.org/abs/1103.1469v2

Mathematics

Differential Geometry

11 pages. Missing citation supplied in new (April 2, 2012) version

Scientific paper

We use Ilmanen's elliptic regularization to prove that for an initially
smooth mean convex hypersurface in Euclidean n-space moving by mean curvature
flow, the surface is very nearly convex in a spacetime neighborhood of every
singularity. Previously this was known only (i) for n < 7, and (ii) for
arbitrary n up to the first singular time.

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