``A priori'' estimates, uniqueness and existence of positive solutions of Yamabe type equations on complete manifolds (Q880118)

The Yamabe problem is the search of a metric having constant scalar curvature in each conformal class of Riemannian metrics defined on some manifold. On a compact Riemannian manifold, it is known after the works of T. Aubin and R. Schoen that such a metric always exists, however on complete noncompact manifolds such a metric does not exist necessarily and it is an open problem under which conditions such a metric exists. In the paper under review the authors study the asymptotic behaviour of a Yamabe type problem on complete manifolds and prove an interesting comparison result as well as an existence and uniqueness result under suitable Ricci assumptions.