On short-time existence for mean curvature flow of surface clusters with triple edges

We will discuss two recent short-time existence results for (1) mean curvature of surface clusters, where n-dimensional surfaces in R^{n+k}, are allowed to meet at equal angles along smooth edges, and (2) for planar networks, where curves are initially allowed to meet in multiple junctions that resolve immediately into triple junctions with equal angles. The first result, which is joint work with B. White, follows from an elliptic regularisation scheme, together with a local regularity result for flows with triple junctions, which are close to a static flow of the half-planes. The second result, which is joint work with T. Ilmanen and A.Neves, relies on a monotonicity formula for expanding solutions and a local regularity result for the network flow.