Loss of convexity for a modified Mullins-Sekerka model arising in diblock copolymer melts

This modified (two-sided) Mullins-Sekerka model is a nonlocal evolution mod el for closed hypersurfaces, which appears as a singular limit of a modifie d Cahn-Hilliard equation describing micro-phase separation of diblock copol ymer. Under this evolution the propagating interfaces maintain the enclosed volumes of the two phases. We will show by means of an example that this m odel does not preserve convexity in two space dimensions.