Numerical evidence of fattening for the mean curvature flow

In this paper we describe some numerical simulations in the context of mean curvature flow. We recover a few different approaches in modelling the evolution of an interface $\Sigma$ which evolves according to the law: $V = \kappa + g$ where $V$ is the velocity in the inward normal direction, $\kappa$ is the sum of the principal curvatures and $g$ is a given forcing term. We will discuss about the phenomenon of fattening or nonuniqueness of the solution, recovering what is known about this subject. Finally we show some interesting numerical simulations that suggests evidence of fattening starting from different initial interfaces. Of particular interest is the result obtained for a torus in $\bold R^4$ which would be a first example of a regular and compact surface showing evidence of fattening in the case of pure motion by mean curvature (no forcing term).