2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76096In this note we study the conformal metrics of constant $Q$ curvature on closed locally conformally flat manifolds. We prove that for a closed locally conformally flat manifold of dimension $n\geq 5$ and with Poincarë exponent less than $\frac {n-4}2$, the set of conformal metrics of positive constant $Q$ and positive scalar curvature is compact in the $C^\infty$ topology.17 pages. to appear in CVPDEDifferential GeometryAnalysis of PDEs53C21, 58J05text