Variational Techniques for the Prescribed $Q$-Curvature Equation

MINI-COURSE IN GEOMETRIC PDE
Topic:Variational Techniques for the Prescribed $Q$-Curvature Equation
Speaker:Andrea Malchiodi
Affiliation:Scuola Internazionale Superiore di Studi Avanzati, Italy and Member, School of Mathematics
Date:Tuesday, October 21
Time/Room:1:30pm - 3:30pm/S-101

After recalling the definition of $Q$-curvature and some applications, we will address the question of prescribing it through a conformal deformation of the metric. We will address some compactness issues, treated via blow-up analysis, and then study the problem, which has variational structure, using a Morse-theoretical approach.