Mean curvature flow and other evolution equations

Course at Tübingen University, Winter 2020/2021. The course treats the deformation of hypersurfaces along their mean curvature vector in Euclidean space and in Riemannian manifolds. We investigate the interplay between geometric structures and the analytical properties of systems of quasi-linear parabolic partial differential equations. Different techniques for the establishment of estimates on the behavior of solutions are developed, for example curvature estimates, density estimates and long-term asymptotical behavior of special solutions. The lectures are part of a master course at the University of Tübingen.