GAMP/TFA seminar by Alexander Friedrich (U Copenhagen)
GAMP/TFA (Geometric Analysis and Mathematical Physics/Topology & Functional Analysis) Seminar.
Speaker: Alexander Friedrich (U Copenhagen)
Title: How to Plant a Bubble Tree
Abstract: Trying to find surfaces which minimize the Willmore energy we are naturally led to weak convergence in W2,2 away from finitely many singular points. Unfortunately this convergence leaves the class of surfaces and yields stratified surfaces. We will explore how this stratification comes about, which problems it entails and what we can do to prevent these. If time permits we will also introduce generalizations to the Willmore energy, that draw their inspiration from General Relativity and Biophysics. Since the Willmore energy will be the dominating term, and as the stratification is inherent to the convergence, we face the same problems as in the classical case. However, experiments in Biophysics seem to indicate that this is at times a feature and not a bug.