Flat flow is motion by crystalline curvature for curves with crystalline energies
It is shown that, for interface energies which are crystalline, motion of curves in the plane by crystalline curvature typically coincides with their flat curvature flow. An interface energy function is called crystalline in the case that its equilibrium crystal shape (Wulff shape) is a polygon. Motion by crystalline curvature results from integration of coupled systems of ordinary differential equations as set forth independently in [\textit{S. Angenent} and \textit{M. E. Gurtin}, II: Arch. Ration. Mech. Anal. 108, No. 4, 323-391 (1989; Zbl 0723.73017) and \textit{J. E. Taylor}, Proc. Symp. Pure Math. 54, 417-438 (1993; Zbl 0823.49028)]. Flat curvature flows are the limits of sequences of variational minimizations as set forth in [\textit{F. Almgren, J. E. Taylor}, and \textit{L. Wang}, Curvature driven flows: A variational approach, SIAM J. Control Optimization 31, No. 2, 387-438 (1993; Zbl 0783.35002)].
scientific article; zbMATH DE number 844212