Implicit time discretization for mean convex sets

In 1995, Luckhaus and Sturzenhecker proved that the implicit time discretization for mean curvature flow converges to a distributional solution provided that the time-integrated perimeters of the approximations converge to those of the limit. In this talk I will show that in the case of strictly mean convex initial conditions, this condition is indeed verifiable. The proof establishes, by compensated compactness techniques, the strict convergence of the arrival time functions. This is joint work with Guido De Philippis.