Let $(M,g)$ be a smooth, closed Riemannian manifold with dimension $n>4$. Define the $Q$-curvature through the formula

$Q = \Delta R + \frac{n^3-4n^2+16n-16}{(n-1)(n-2)^2} R^2 - \frac{8(n-1)}{(n-2)^2}|Ric|^2,$

where $\Delta = -div\nabla$, $R$ is the scalar curvature, and $|Ric|$ is the norm of the Ricci tensor. This quantity arises in many problems in conformal differential geometry. The question is whether or not a uniform sup-norm bound on a sequence of $Q$ curvatures implies there exists a uniform sup-norm bound on the corresponding scalar curvatures, provided that all of the scalar curvatures change sign?