On the prescribed scalar curvature problem on Sn: Part 1, asymptotic estimates and existence results

There have been many works on the problem of finding a conformal metric on the standard sphere Sn,n≥3Sn,n≥3, when the prescribed scalar curvature function is flat near its critical points with order of flatness β  . All the existence results up to this research concern the case 1<β1β>1. Moreover, we establish (in this first part) existence results concerning some cases of β≥nβ≥n.