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Let $(M,g)$ a n-dimensional Riemannian manifold, $n\neq 4$, and $h=u^{\frac{4}{n-4}}g$. Then the formula that connect the Panitz-Branson opertator $P_g$ and the Q-curvature $Q_{h}$ is

$Q_h=\frac{2}{n-4}u^{-\frac{n+4}{n-4}}P_{g}u$.

Where is a proof of this fact?

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  • $\begingroup$ $Q_g$ should appear int the formula like the scalar curvature for the conformal laplacian. I think you will ding what you what in the original paper of Branson, citeseerx.ist.psu.edu/viewdoc/…, see 1.10 for instance $\endgroup$
    – Paul
    Commented Oct 7, 2016 at 14:45

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