Sign of Green's function of Paneitz operators and the Q curvature
  In a conformal class of metrics with positive Yamabe invariant, we derive a necessary and sufficient condition for the existence of metrics with positive Q curvature. The condition is conformally invariant. We also prove some inequalities between the Green's functions of the conformal Laplacian operator and the Paneitz operator. 
Fengbo Hang and Paul C. Yang
math.DG math.AP