Appears in collection : Not Only Scalar Curvature Seminar

We will start by recalling some basics about smooth versus weak solutions of inverse mean curvature flow (IMCF) from the classical works by Huisken and Ilmanen, where the level set solutions are applied to prove the Riemannian Penrose inequality. But this notion of weak solutions cannot work in milder regularity settings, like those needed to model crystal growth, which require an anisotropic framework (with no regularity nor ellipticity extra requirements), and where the objects to evolve are at most Lipschitz regular. In this a priori unfriendlier scenario, during the second part of the talk, we will explain how we still manage to find a good notion of weak IMCF coming out of a crystal. This is based on joint works with Salvador Moll and Marcos Solera.