On the avoidance principle for codimension 1 space-time Brakke flows

Abstract

We prove that the spacetime Brakke flow constructed by Buet et al. is non-trivial as long as the initial varifold is a union of boundaries of domains of finite perimeter. In the codimension 1 setting, we show that, starting from a smooth boundary, the support of the mass measure of the spacetime Brakke flow coincides with the support of the classical mean curvature flow.