Mean curvature flow with triple junctions in higher space dimensions
  We consider mean curvature flow of n-dimensional surface clusters. At (n-1)-dimensional triple junctions an angle condition is required which in the symmetric case reduces to the well-known 120 degree angle condition. Using a novel parametrization of evolving surface clusters and a new existence and regularity approach for parabolic equations on surface clusters we show local well-posedness by a contraction argument in parabolic Hoelder spaces. 
Daniel Depner, Harald Garcke and Yoshihito Kohsaka
math.AP