Convergence of a crystalline algorithm for the motion of a simple closed convex curve by weighted curvature
It provides a rigorous convergence proof for a numerical method used in materials science and geometry, addressing a known gap in the analysis of crystalline algorithms.
The paper proves the convergence of a crystalline algorithm for computing motion by weighted mean curvature for simple closed convex curves in the plane, validating the numerical method for anisotropic surface energy evolution.
Motion by weighted mean curvature is a geometric evolution law for surfaces and represents steepest descent with respect to anisotropic surface energy. It has been proposed that this motion could be computed numerically by using a "crystalline" approximation to the surface energy in the evolution law. In this paper we prove the convergence of this numerical method for the case of simple closed convex curves in the plane.