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Presented By: Department of Mathematics

Geometry

Riemannian manifolds with positive Yamabe invariant and Paneitz operator

For a compact 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 characterizations for the Paneitz operator and Q-curvature in higher dimensions. For a smooth compact 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, we also study the relationship between different conformal invariants associated to the Q-curvature. This is joint work with Matt Gursky and Fengbo Hang. Speaker(s): Yueh-Ju Lin (UM)

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