|Dept.||University of Wisconsin|
In this talk, we discuss the crystalline mean curvature flow with nonlocal forcing given by a volume constraint. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Based on the discrete-in-time approximation, we establish the global-in-time existence and regularity for a class of initial data with the reflection property. This talk is based on joint work with Inwon Kim (UCLA) and Norbert Pozar (Kanazawa University).