REMARKS ON THE CONVERGENCE OF AN ALGORITHM FOR CURVATURE-DEPENDENT MOTIONS OF HYPERSURFACES

We consider a threshold-type algorithm for curvature-dependent motions (CDM for short) of hypersurfaces. This algorithm was numerically studied by Kimura - Notsu [13], Esedoglu - Ruuth - Tsai H and Mohammad - Svadlenka [16], where they used the signed distance function as the level set function for CDM. The convergence of this algorithm and its optimal rate have been considered in Ishii - Kimura [12]. In this paper we give different approaches to the optimal rate of convergence to the smooth and compact CDM from [12]. As for the optimality, we give a more precise estimate than that in [12].