Geometric Analysis Seminars-Rigidity theorems about Q-curvature

Abstract:

In this talk, we will introduce some rigidity theorems on complete and conformally flat manifolds with help of Q-curvature. We introduce a new volume entropy to give a sufficient and necessary condition for the ”normal” metric. Meanwhile, with help of geometric measure theory, we give a distance comparison identity on such manifolds which generalize the result of Li-Tam(1991, JDG) to higher dimensions. Finally, we want to talk about higher order Bol’s inequality which is a joint work with Professor Juncheng Wei.