Convergence of an Algorithm for the Anisotropic and Crystalline Mean Curvature Flow

The volume preserving crystalline mean curvature ow of convex sets in R

We prove the existence of a volume preserving crystalline mean curvature at ow starting from a compact convex set C ⊂ R and its convergence, modulo a time-dependent translation, to a Wul shape with the corresponding volume. We also prove that if C satis es an interior ball condition (the ball being the Wul shape), then the evolving convex set satis es a similar condition for some time. To prove...

The Crystalline Algorithm for Computing Motion by Curvature

Motion by (weighted) mean curvature is a geometric evolution law for surfaces, representing steepest descent with respect to (anisotropic) surface energy. The crystalline algorithm is a numerical method for computing this motion. The main idea of this method is to solve the analogous evolution law for a crystalline surface energy which approximates the underlying smooth one. We have recently ex...

The volume preserving crystalline mean curvature flow of convex sets in R

We prove the existence of a volume preserving crystalline mean curvature flat flow starting from a compact convex set C ⊂ R and its convergence, modulo a time-dependent translation, to a Wulff shape with the corresponding volume. We also prove that if C satisfies an interior ball condition (the ball being the Wulff shape), then the evolving convex set satisfies a similar condition for some time...

Convergence of an algorithm for anisotropic mean curvature motion

We give a simple proof of convergence of the anisotropic variant of a wellknown algorithm for mean curvature motion, introduced in 1992 by Merriman, Bence and Osher. The algorithm consists in alternating the resolution of the (anisotropic) heat equation, with initial datum the characteristic function of the evolving set, and a thresholding at level 1/2.

Anisotropic and Crystalline Mean Curvature Flow