By YanYan Li, Rutgers University

Let $(M,g)$ be an $n\ge 5$ dimensional smooth compact Riemannian manifold of positive Yamabe type, which is not conformally equivalent to the standard sphere. We prove compactness of conformal metrics of $g$ with positive constant Q-curvature provided that $(M,g)$ is locally conformally flat, or $n=5,6,7$. For $n\ge 8$, we prove the compactness result provided that the Weyl tensor of $g$ does not vanish anywhere. This is a joint work with Jingang Xiong.