Lectures on Mean Curvature Flows

The curve shortening flow for convex curves The short time existence and the evolution equation of curvatures Contraction of convex hypersurfaces Monotonicity and self-similar solutions Evolution of embedded curves or surfaces (I) Evolution of embedded curves and surfaces (II) Evolution of embedded curves and surfaces (III) Convexity estimates for mean convex surfaces Li-Yau estimates and type II singularities The mean curvature flow in Riemannian manifolds Contracting convex hypersurfaces in Riemannian manifolds Definition of center of mass for isolated gravitating systems References Index.