Introduction to Variational and Level Set Methods for Geometric Flows

What it is about

You learn analytical and variational methods for the study of geometric flows. The focus is on Level-Set methods, viscosity solutions of degenerate parabolic equations, and variational formulations of the Mean-Curvature Flow. In the end you will be able to understand existence and uniqueness statements for generalized Level-Set Flows and cope with concepts such as Weak–Strong-Uniqueness, Fattening, and Minimising Movements.

What you will be able to do

• Apply viscosity theory to degenerate parabolic equations
• Use Level-Set approach to describe generalized geometric motions
• Analyze existence and uniqueness statements for Level-Set Flows
• Understand the concept Weak–Strong-Uniqueness
• Classify fattening phenomena
• Explain Minimising-Movements schemes and their convergence for Mean-Curvature-Flow
• Familiarity with Flat Flows, Perimeter Descent and nonlocal/anisotropic extensions

What the module consists of

• VorlesungPresents the theoretical content, concepts and examples
• Übung/Practice SessionsDeepening the lecture content through exercises and self-check; exercise sheets with solutions

Teaching method

• Vortrag mit BeispielenTo introduce the content and illustrate the methods
• Diskussion mit StudierendenTo deepen and critically engage with the topics
• Übungsblätter mit LösungenFor independent deepening and checking understanding