On the prescribed scalar curvature problem on 4-manifolds
This work gives a complete and detailed proof of the result stated in the appendix of the paper of \textit{A. Bahri} and \textit{J. M. Coron} [J. Funct. Anal. 95, No. 1, 106-172 (1991; Zbl 0722.53032)]. The key part in the proof is to find a good pseudo-gradient flow. This is hard work. To do this, they need to find a good Morse lemma at bubbles. It is well-known that once we have a good flow, we can establish the critical point theory for our functional. The other thing is that the authors treat the Kazdan-Warner problem on general 4-manifolds, using conformal coordinates. As the authors state in their paper, their proof is based on recent work of \textit{A. Bahri} [Duke Math. J. 81, No. 2, 323-466 (1996; Zbl 0856.53028)].
scientific article; zbMATH DE number 943721