Inserted: 4 feb 2017
Last Updated: 4 feb 2017
We prove the existence of a weak global in time mean curvature flow of a bounded partition of space using the method of minimizing movements. The result is extended to the case when suitable driving forces are present. We also show that the minimizing movement solution starting from a partition made by a union of bounded convex sets at a positive distance agrees with the classical mean curvature flow, and the motion is stable with respect to the Hausdorff convergence of the initial partition.
Keywords: minimizing movements, mean curvature flow, partitions