Some Other Important Topics

Abstract

We have already mentioned extensions of various results for compact manifolds to complete manifolds. It is clear that one should restrict oneself to only certain sorts of noncompact Riemannian manifolds to have a hope of obtaining results. Let us mention in particular the possibilities of examining manifolds with finite volume, those with prescribed asymptotic behaviour at infinity, for example quadratic decay,1 quadratic curvature decay, volume behaviour, Euclidean asymptoticity, etc.