Weak Solution Concepts for Mean Curvature Flow

In this talk, I introduce and motivate mean curvature flow. It appears in numerous applications in Material Science (soap bubbles and films, fluid mixing, poly crystals), general physics (black holes), image processing (denoising, edge filters) and machine learning (classification and clustering).

Unfortunately, this parabolic evolution on manifolds develops singularities from dimension three onward, even if started from smooth initial data. This is physically meaningful and desired but requires us to study weak solution concepts. I present the most important ones and prove partial equivalences. The equivalence proofs are joint work with Tim Laux.