Conformally Prescribed Scalar Curvature on Orbifolds

Abstract

AbstractWe 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 $$n \ge 4$$ n ≥ 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 $$\textrm{U}(2)$$ U ( 2 ) -invariant Leray–Schauder degree for a family of negative-mass orbifolds found by LeBrun.