Nonexistence of complete conformal metrics with prescribed scalar curvatures on a manifold of nonpositive curvature

Let (M, g) be a complete simply-connected Riemannian manifold with nonpositive curvature, k its scalar curvature, and K a smooth function onM.We obtain a nonexistence result of complete metrics on M conformal to g and with K as their scalar curvature.  2004 Elsevier Inc. All rights reserved