Curves and Networks in Geometric Analysis

Existence of Brakke flow solutions from surface clusters via elliptic regularisation

speaker: Felix Schulze (University College London)

abstract: We consider clusters of n-dimensional surfaces in any codimension where away from a closed set with zero (n-1)-dimensional Hausdorff measure, along the smooth boundaries three sheets meet under an equal angle. We show that under a topological condition, there exists a Brakke flow starting from such a cluster, which attains the initial cluster in C^\infinity away from the junctions and in C¹ at the triple junctions. For curves (i.e. networks) in any codimension the assumption of equal angles initially is not necessary, as long as they are positive. The proof uses elliptic regularisation and a recent regularity result for mean curvature flow with triple edges. This is joint work with B. White.

timetable:
Tue 27 Jun, 15:00 - 15:50, Aula Dini
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