On constant Q-curvature metrics with isolated singularities and a related fourth order conformal invariant

Abstract: The Q-curvature of a Riemannian manifold is a higher order analog of its scalar curvature, and so many people have over the last two decades proven results about Q-curvature mirroring theorems about scalar curvature. I will present two such results. First, I will describe a refined asymptotic expansion of isolated singularities in the conformally flat case, similar to work of Caffarelli, Gidas and Spruck in the scalar curvature setting. Then I will describe a conformal invariant and prove a convergence result similar to a theorem of Schoen.

Mathematics

Audience: researchers in the topic

Online Seminar "Geometric Analysis"

Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

Registration and links to videos available at blatt.sbg.ac.at/onlineseminar.php