Lojasiewicz inequalities near simple bubble trees

Abstract: In the study of (almost-)critical points of an energy functional one is often confronted with the problem that a weakly-obtained limiting object does not have the same topology. For example sequences of almost-harmonic maps from a surface will in general not converge to a single harmonic map but rather to a whole bubble tree of harmonic maps, which cannot be viewed as an object defined on the original domain.

One of the consequences of this phenomenon is that one of the most powerful tools in the study of (almost-)critical points and gradient flows of analytic functionals, so called Lojasiewicz-Simon inequalities, no longer apply.

In this talk we discuss a method that allows us to prove such Lojasiewicz inequalities for the harmonic map energy near simple trees and explain how these inequalities allow us to prove convergence of solutions of the corresponding gradient flow despite them forming a singularity at infinity.

differential geometry

Audience: researchers in the topic

---

Pangolin seminar

Series comments: TIME HAS CHANGED: 15:30 Paris 10:30AM Rio de Janeiro

Description: Differential geometry seminar

Zoom link posted on the webpage 15 minutes before each lecture: https://sites.google.com/view/pangolin-seminar/home

---