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 extremal problem for a new functional involving the Paneitz operator. 
Fengbo Hang and Paul C. Yang
math.DG math.AP