Calculus of Variations and Geometric Measure Theory

G. De Philippis - T. Laux

Implicit time discretization for the mean curvature flow of outward minimizing sets

created by dephilipp on 07 Jun 2018
modified on 02 May 2019


Accepted Paper

Inserted: 7 jun 2018
Last Updated: 2 may 2019

Journal: Ann. Sc. Norm. Super. Pisa Cl. Sci
Year: 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.