CONFORMAL DEFORMATION TO PRESCRIBED SCALAR CURVATURE ON COMPLETE NONCOMPACT RIEMANNIAN MANIFOLDS WITH NONPOSITIVE CURVATURE

Dedicated to Professor Hideki Ozeki on his 60th birthday

Abstract

We consider the problem of deforming the metric on a complete negatively curved manifold conformally to another complete metric whose scalar curvature is positive in an unbounded domain. We also consider the case of the Euclidean space.