Convergence of a threshold-type algorithm for curvature-dependent motions of hypersurfaces

Abstract

We consider a threshold-type algorithm for curvature-dependent motions of hypersurfaces. This algorithm was numerically studied by Kimura–Notsu [11], Esedoḡlu–Ruuth–Tsai [4] and Mohammad–Švadlenka [13], where they used the signed distance function as the level set function for curvature-dependent motions. In this artcle we present the convergence and its optimal rate of this algorithm, according to Ishii–Kimura [9] and Ishii–Izumi [10].