Comptes Rendus
Partial Differential Equations/Differential Geometry
On the prescribed Q-curvature problem on Sn
[Sur le problème de la Q-courbure prescrite sur Sn]
Comptes Rendus. Mathématique, Volume 348 (2010) no. 11-12, pp. 635-638.

Dans cette Note nous prescrivons une courbure du quatrième order-la Q-courbure sur la sphère standard de dimension n5. Sous une « condition de platitude » d'ordre β[n4,n[ au voisinage de chaque point critique de la fonction Q-courbure prescrite, nous prouvons un nouveau résultat d'existence grâce à une formule de type Euler–Hopf. Notre argument donne une minoration du nombre des métriques ayant la même Q-courbure.

In this Note we prescribe a fourth order curvature – the Q-curvature on the standard n-sphere, n5. Under the “flatness condition” of order β, n4β<n near each critical point of the prescribed Q-curvature function, we prove new existence result through an Euler–Hopf type formula. Our argument gives a lower bound on the number of conformal metrics having the same Q-curvature.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.03.018

Hichem Chtioui 1 ; Afef Rigane 1

1 Département de Mathématiques, Faculté des Sciences de Sfax, Route Soukra, Sfax, Tunisia
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Hichem Chtioui; Afef Rigane. On the prescribed Q-curvature problem on $ {S}^{n}$. Comptes Rendus. Mathématique, Volume 348 (2010) no. 11-12, pp. 635-638. doi : 10.1016/j.crma.2010.03.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.03.018/

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