Q-Curvature, Conformal Invariants, and Deformation Problems
Speaker: Yueh-Ju Lin,
Abstract: For a closed Riemannian manifold of dimension at least three, we know that positive Yamabe invariant implies the existence of a conformal metric with positive scalar curvature. As a higher order analogue, we seek for similar characterisations 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. In addition, motivated by the early work of Fischer-Marsden on “vacuum static spaces”, we study “Q-singular spaces” through general deformations of Q-curvature. We prove local surjectivity for non-Q-singular spaces and rigidity of flat manifolds. The first part of the talk is joint work with Matt Gursky and Fengbo Hang. The second part is joint work with Wei Yuan.
Room Reservation Information
Room Number: 106 McAllister
Time: 2:30pm - 3:30pm