Q‐Curvature on a Class of Manifolds with Dimension at Least 5

For a smooth compact Riemannian manifold with positive Yamabe invariant, positive Q ‐curvature, and dimension at least 5, we prove the existence of a conformal metric with constant Q ‐curvature. Our approach is based on the study of an extremal problem for a new functional involving the Paneitz operator.