News Overview

We are delighted to announce the compact course on The gradient flow structure of mean curvature flow by Prof Tim Laux, expert for applied geometric analysis at Uni­ver­si­ty of Bonn, who is currently staying in Hei­del­berg as a guest of STRUCTURES. The courses will take place from Tuesday, April 18 to April 26, 14h-16h, respectively. Please find the abstract attached below:

Title: The gradient flow structure of mean curvature flow
Abstract: Mean curvature flow is the most basic geometric evolution equation for embedded surfaces. Folklore says that it can be viewed as a gradient flow. This course aims at making this statement more precise and harnessing this structure for rigorous analysis. After a brief introduction to the field, I will present some of the ideas behind the (conditional) existence and (weak-strong) uniqueness theory for solutions to mean curvature flow. Focusing on the simple two-phase case, i.e., the evolution of a closed hypersurface, allows for a self-contained and concise presentation, which is accessible for graduate students (master or PhD) with some background in PDEs and functional analysis. The course is structured into four lectures as follows. The first lecture provides an overview, basic examples, and some motivation from numerics and data science. In the second lecture, I'll discuss different weak solution concepts, present a (conditional) closure theorem and relate different solution concepts. The third lecture is devoted to the weak-strong uniqueness principle via a concept of gradient flow calibrations. In the last lecture, I'll show how to use this structure for proving optimal convergence rates for numerical schemes.