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 textrm{U}(2)-invariant Leray–Schauder degree for a family of negative-mass orbifolds found by LeBrun.