## Multiphase Mean Curvature Flow: Uniqueness Properties of Weak Solution Concepts and Phase-Field Approximations

Topology changes occur naturally in geometric evolution equations like mean curvature flow. As classical solution concepts break down at such geometric singularities, the use of weak solution concepts becomes necessary in order to describe topological changes.

For two-phase mean curvature flow, the theory of viscosity solutions by Chen-Giga-Goto and Evans-Spruck provides a concept of weak solutions with basically optimal existence and uniqueness properties.