Level Set and Variational Methods for Curvature Flows

We review the classical viscosity level set methods for generalised mean curvature flows, the minimising movements variational approximation of level set flows, and a more recent distributional approach to deal with the well-posedness of crystalline curvature motions. We will also show how the latter distributional approach can be extended to some nonlocal motions. Finally, as time permits, we will present an anisotropic variant of the Ilmanen elliptic regularisation scheme and, relying on the aformentioned distributional formulation, we will show its convergence to level set solutions.