Compactness Within the Space of Complete, Constant <i>Q</i>-Curvature Metrics on the Sphere with Isolated Singularities

Abstract In this paper, we consider the moduli space of complete, conformally flat metrics on a sphere with $k$ punctures having constant positive $Q$-curvature and scalar curvature. Previous work has shown that such admit an asymptotic expansion near each puncture, allowing one to define necksize singular point. We prove any set in distances between distinct necksizes all remain bounded away from zero is sequentially compact, mirroring theorem D. Pollack about Yamabe metrics. Along way, radial Pohozaev invariant at puncture refine some priori bounds conformal factor, which may be independent interest.