15 jun 2015

8 hours course

Abstract.

The course covers two separate but closely related topics. The first topic is the mean curvature flow in the framework of Geometric Measure Theory due to Brakke. It is a flow of varifold moving by the generalized mean curvature. Starting from a quick review on the necessary tools and facts from Geometric Measure Theory and the definition of the Brakke mean curvature flow, I will give an overview on the proof of the local regularity theorem. The second topic is the reaction-diffusion approximation of phase boundaries with key words such as the Modica-Mortola functional and the Allen-Cahn equation. Their singular perturbation problems are related to objects such as minimal surfaces and mean curvature flows in the framework of Geometric Measure Theory.