%0 Journal Article %A Schulze, F %A White, B %D 2020 %F discovery:1571171 %I Walter de Gruyter %J Journal für die reine und angewandte Mathematik (Crelles Journal) %N 758 %T A local regularity theorem for mean curvature flow with triple edges %U https://discovery.ucl.ac.uk/id/eprint/1571171/ %V 2020 %X Mean curvature flow of clusters of n-dimensional surfaces in Rn+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. %Z This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.