MCF Winter 2020

V5B1 - Advanced Topics in Analysis and Partial Differential Equations at Uni Bonn

Please also visit the official webpages at basis.uni-bonn.de and eCampus.uni-bonn.de

The course will be given online.
Please contact me if you need a password and don't have access to eCampus.

About the Course

In this course, I want to give an overview on the analysis of the mean curvature flow equation, in particular from the point of view of PDEs and calculus of variations. Mean curvature flow arises in many applications inside and outside of mathematics and has been widely studied over the last decades. We will start understanding the PDE by studying strong solutions, the evolution of various geometric quantities, and constructing special solutions. Then, we will discuss several weak solution concepts, namely viscosity solutions based on the comparison principle, distributional solutions based on the gradient flow structure, and varifold solutions based on local energy dissipation. We will show that mean curvature flow arises as the singular limit of simple PDEs, as the limit of (sequences of) variational problems, and as the limit of the computationally efficient thresholding scheme. If time permits, we will discuss multiphase mean curvature flow.

Prerequisites

Working knowledge in Functional Analysis, PDEs, and basic knowledge of Differential Geometry are assumed. Basic concepts from Geometric Measure Theory are useful but not necessary to follow the course.

Lectures

Wednesdays 10am-noon
Fridays 10am-noon

Office Hours

You can find me online by appointment or during my regular office hour on

We noon-1pm