Inserted: 7 jun 2018
Last Updated: 7 jun 2018
In this note we analyze the Almgren-Taylor-Wang scheme for mean curvature flow in the case of outward minimizing initial conditions. We show that the scheme preserves the outward minimizing property and, by compensated compactness techniques, that the arrival time functions converge strictly in \(BV\). In particular, this establishes the convergence of the time-integrated perimeters of the approximations. As a corollary, the conditional convergence result of Luckhaus-Sturzenhecker becomes unconditonal in the outward minimizing case.