Conformally prescribed scalar curvature on orbifolds

Abstract

We study the prescribed scalar curvature problem in a conformal class on orbifolds with isolated singularities. We prove a compactness theorem in dimension $4$, and an existence theorem which holds in dimensions $n\ge 4$. This problem is more subtle than the manifold case since the positive mass theorem does not hold for ALE metrics in general. We also determine the $\mathrm{U}(2)$-invariant Leray-Schauder degree for a family of negative-mass orbifolds found by LeBrun.

39 pages