The problem studied here focuses on a compact manifold M without boundary in which the Riemannian metric g is on Λ = M−{p1, p2, ..., pk}. Near the pi’s, g has a particular type of singularity in which locally M = (0, δ)x×Y where Y is a Riemannian manifold with metric h. Calculation techniques involving Christoffel symbols, scalar curvature, and the Lapalacian of the manifold are used to reduce the Yamabe equation to a system of partial differential equations. After assuming that a function u… CONTINUE READING