Title: Nonexistence of complete conformal metrics with prescribed scalar curvatures on a manifold of nonpositive curvature
Abstract: Let (M,g) be a complete simply-connected Riemannian manifold with nonpositive curvature, k its scalar curvature, and K a smooth function on M. We obtain a nonexistence result of complete metrics on M conformal to g and with K as their scalar curvature.