Some remarks on the level set flow by anisotropic curvature

Abstract

We show that almost all level sets of the unique viscosity solution for general anisotropic mean curvature flow satisfy a weak form of the flow equation. This generalizes the case of isotropic mean curvature flow studied by Evans and Spruck, in which a relation between the viscosity solution and Brakke's varifold mean curvature flow is established.