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

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

We give a simple proof of convergence of the anisotropic variant of a well-known 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

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.

Crystalline mean curvature flow of convex sets

We prove a local existence and uniqueness result of crystalline mean curvature flow starting from a compact convex admissible set in R . This theorem can handle the facet breaking/bending phenomena, and can be generalized to any anisotropic mean curvature flow. The method provides also a generalized geometric evolution starting from any compact convex set, existing up to the extinction time, sa...

Existence and uniqueness for planar anisotropic and crystalline curvature flow

We prove short-time existence of φ-regular solutions to the planar anisotropic curvature flow, including the crystalline case, with an additional forcing term possibly unbounded and discontinuous in time, such as for instance a white noise. We also prove uniqueness of such solutions when the anisotropy is smooth and elliptic. The main tools are the use of an implicit variational scheme in order...