Abstract
We deal with the Q-curvature problem on a 4-dimensional compact Riemannian manifold (M,g) with ∫MQgdVg=8π2 and positive Paneitz operator Pg. Let Q̃ be a positive smooth function. The question we consider is, when can we find a metric g̃ which is conformal to g, such that Q̃ is just the Q-curvature of g̃. A sufficient condition to this question is given in this paper.
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