On the prescribed scalar curvature problem on 4-manifolds
type: Item
instance of: scholarly article
title: On the prescribed scalar curvature problem on 4-manifolds
zbMATH Open document ID: 0862.53034
DOI: 10.1215/S0012-7094-96-08420-3
author: Mohamed Ben Ayed
author: Yansong Chen
author: Hichem Chtioui
author: Mokhless Hammami
published in: Duke Mathematical Journal
publication date: 1997-05-25T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 943721
zbMATH Keywords: scalar curvature
zbMATH Keywords: conformal normal coordinates
zbMATH Keywords: critical point theory
reviewed by: Li Ma
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 943721