On the prescribed scalar curvature problem on $ {S}^{n}$: The degree zero case

Ben Mahmoud, Randa; Chtioui, Hichem; Rigane, Afef

doi:10.1016/j.crma.2012.06.012

Partial Differential Equations/Differential Geometry

On the prescribed scalar curvature problem on

S^{n}

: The degree zero case
[Sur le problème de courbure scalaire prescrite sur

S^{n}

: Le cas de degré zéro]

Présenté par : Jean-Pierre Demailly

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

Comptes Rendus. Mathématique, Tome 350 (2012) no. 11-12, pp. 583-586.

Résumé
Abstract

Dans cette Note nous considérons le problème dʼexistence de métriques conformes avec courbure scalaire prescrite, sur la sphère standard $S^{n}$ , $n ⩾ 3$ . 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].

In this Note, we consider the problem of the existence of conformal metrics with prescribed scalar curvature on the standard sphere $S^{n}$ , $n ⩾ 3$ . 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].

Reçu le : 2012-06-02
Accepté le : 2012-06-27
Publié le : 2012-06-01

DOI : 10.1016/j.crma.2012.06.012

Affiliations des auteurs :

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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     title = {On the prescribed scalar curvature problem on $ {S}^{n}$: {The} degree zero case},
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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, Tome 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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