A local regularity theorem for mean curvature flow with triple edges

2016/05/21 by Schulze, Felix, White, Brian · 3 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1605.06592

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.

Cited by

• The Bounded Diameter Conjecture and Sharp Geometric Estimates for Mean Curvature Flow
• Mean curvature flow through singularities
• The Dirichlet problem for the minimal surface system on smooth domains

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