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The \(Q\)-curvature on a 4-dimensional Riemannian manifold \((M,g)\) with \(\int_M QdV_g = 8\pi^2\). (English) Zbl 1254.53065

Summary: We deal with the \(Q\)-curvature problem on a 4-dimensional compact Riemannian manifold \((M,g)\) with \(\int_M Q_g dV_g= 8\pi^2\) and positive Paneitz operator \(P_g\). Let \(\widetilde Q\) be a positive smooth function. The question we consider is, when can we find a metric \(\widetilde g\) which is conformal to \(g\), such that \(\widetilde Q\) is just the \(Q\)-curvature of \(\widetilde g\). A sufficient condition to this question is given in this paper.

MSC:

53C20 Global Riemannian geometry, including pinching
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