Partial Differential Equations/Differential Geometry
On the prescribed scalar curvature problem on Sn: The degree zero case
Comptes Rendus. Mathématique, Volume 350 (2012) no. 11-12, pp. 583-586.

In this Note, we consider the problem of the existence of conformal metrics with prescribed scalar curvature on the standard sphere Sn, n3. We give new existence and multiplicity results based on a new Euler–Hopf formula type. Our argument also has the advantage of extending the well known results due to Y. Li (1995) [10].

Dans cette Note nous considérons le problème dʼexistence de métriques conformes avec courbure scalaire prescrite, sur la sphère standard Sn, n3. Nous donnons de nouveaux résultats dʼexistence et de multiplicité reposant sur un nouveau type de formule dʼEuler–Hopf. Nos arguments ont également lʼavantage dʼétendre des résultats bien connus de Y. Li (1995) [10].

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2012.06.012
Ben Mahmoud, Randa 1; Chtioui, Hichem 2; Rigane, Afef 1

1 Department of Mathematics, Faculty of Sciences of Sfax, Route of Soukra, Sfax, Tunisia
2 Department of Mathematics, King Abdulaziz University, P.O. 80230, Jeddah, Saudi Arabia
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Ben Mahmoud, Randa; Chtioui, Hichem; Rigane, Afef. On the prescribed scalar curvature problem on $ {S}^{n}$: The degree zero case. Comptes Rendus. Mathématique, Volume 350 (2012) no. 11-12, pp. 583-586. doi : 10.1016/j.crma.2012.06.012. http://www.numdam.org/articles/10.1016/j.crma.2012.06.012/

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