A local regularity theorem for mean curvature flow with triple edges
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.
Keywords
Cite
@article{arxiv.1605.06592,
title = {A local regularity theorem for mean curvature flow with triple edges},
author = {Felix Schulze and Brian White},
journal= {arXiv preprint arXiv:1605.06592},
year = {2017}
}
Comments
Existence proof extended to cover existence of a Brakke flow, starting from a general cluster in arbitrary codimension. Added details in proof of initial smoothness. Presentation improved, references updated, some typos fixed. 25 pages