No mass drop for mean curvature flow of mean convex hypersurfaces

Abstract

A possible evolution of a compact hypersurface in ${\mathbb{R}}^{n+1}$ by mean curvature past singularities is defined via the level set flow. In the case where the initial hypersurface has positive mean curvature, we show that the Brakke flow associated to the level set flow is actually a Brakke flow with equality. As a consequence, we obtain the fact that no mass drop can occur along such a flow. A further application of the techniques used above is to give a new variational formulation for mean curvature flow of mean convex hypersurfaces