NTU Mathematics Colloquium 1060220
NTU Mathematics Colloquium
演講者：Yueh-Ju Lin (Department of Mathematics, University of Michigan)
講 題：Q-curvature and conformal invariants
時 間：2017年2月20日 (星期一) 10:00 - 11:00 a.m.
摘 要：For a closed Riemannian manifold of dimension at least three, positive Yamabe invariant implies the existence of a conformal metric with positive scalar curvature. As a higher order analogue of this result, we seek for similar characterizations for the Paneitz operator and Q-curvature in higher dimensions. For a smooth closed Riemannian manifold of dimension at least six, we prove that the existence of a conformal metric with positive scalar and Q-curvature is equivalent to the positivity of both the Yamabe invariant and the Paneitz operator.
There are no general existence results for prescribed negative Q-curvature problems. In the second part of my talk, I will show how to use gluing method to construct nontrivial examples of negative constant Q-curvature metrics.
Part of my talk is joint work with Matt Gursky and Fengbo Hang.