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
Mazzeo et al. (Wed,) studied this question.