A local regularity theorem for mean curvature flow with triple edges

Felix Schulze; Brian White

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arXiv · 1605.06592

A local regularity theorem for mean curvature flow with triple edges

Felix Schulze·Brian White

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Abstract

Mean curvature flow of clusters of n-dimensional surfaces in R^{n+k} that meet in triples at equal angles along smooth edges and higher order junctions on lower dimensional faces is a natural extension of classical mean curvature flow. We call such a flow a mean curvature flow with triple edges. We show that if a smooth mean curvature flow with triple edges is weakly close to a static union of three n-dimensional unit density half-planes, then it is smoothly close. Extending the regularity result to a class of integral Brakke flows, we show that this implies smooth short-time existence of the flow starting from an initial surface cluster that has triple edges, but no higher order junctions.

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Felix Schulze, Brian White. 2016-05-21. A local regularity theorem for mean curvature flow with triple edges. https://arxiv.org/abs/1605.06592

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