Constant scalar curvature metrics with isolated singularities

Abstract

We extend the results and methods of [6] to prove the existence of constant positive scalar curvature metrics g which are complete and conformal to the standard metric on S Λ, where Λ is a disjoint union of submanifolds of dimensions between 0 and (N − 2)/2. The existence of solutions with isolated singularities occupies the majority of the paper; their existence was previously established by Schoen [12], but the proof we give here, based on the techniques of [6], is more direct, and provides more information about their geometry. When Λ is discrete we also establish that these solutions are smooth points in the moduli spaces of all such solutions introduced and studied in [7] and [8]