Some results on anisotropic fractional mean curvature flows

TL;DR

This paper proves the consistency of a threshold dynamics algorithm for anisotropic fractional mean curvature flows with forcing, ensuring convexity preservation and uniqueness of evolution for convex sets.

Contribution

It introduces a consistent threshold dynamics algorithm for anisotropic fractional mean curvature flows with forcing and demonstrates convexity preservation and uniqueness.

Findings

Convex sets remain convex during evolution.

The evolution of bounded convex sets is uniquely defined.

The algorithm is consistent with the anisotropic fractional mean curvature flow.

Abstract

We show the consistency of a threshold dynamics type algorithm for the anisotropic motion by fractional mean curvature, in the presence of a time dependent forcing term. Beside the consistency result, we show that convex sets remain convex during the evolution, and the evolution of a bounded convex set is uniquely defined.