ABSTRACT

In this talk, we explore several connections among Q-curvature, scalar curvature, and Ricci curvature. For conformally flat manifolds under appropriate positivity assumptions on the curvatures, we establish control over the growth of integrals over geodesic balls and prove several gap theorems related to Q-curvature. As an application, we settle a conjecture of Yau in this specific geometric setting. This is joint with Juncheng Wei and Xingwang Xu.