A scalar curvature flow in low dimensions

Abstract

Let (Mn, g0) be a n=3,4,5 dimensional, closed Riemannian manifold of positive Yamabe invariant.For a smooth function K > 0 on M we consider a scalar curvature flow, that tends to prescribe K as the scalar curvature of a metric g conformal to g0.We show global existence and in case M is not conformally equivalent to the standard sphere smooth flow convergence and solubility of the prescribed scalar curvature problem under suitable conditions on K.