Convergence of a vector-valued Allen-Cahn system to Brakke's multiphase mean curvature flow

Abstract: Since Ilmanen's pioneering work [J. Differential Geom. 38, 417-461, (1993)] it has been a major open problem to understand the sharp-interface limit of systems of coupled Allen-Cahn equations. We prove - for the first time - a global, unconditional convergence result for such a coupled system and show that the limit is a multiphase mean curvature flow in the sense of Brakke.