Comptes Rendus
Partial Differential Equations
The Webster scalar curvature problem on higher dimensional CR compact manifolds
Comptes Rendus. Mathématique, Volume 345 (2007) no. 1, pp. 11-13

Using a topological arguments due to Aubin–Bahri (1997), we give some existence results for the Webster scalar curvature problem on the 2n+1 dimensional CR compact manifolds locally conformally CR equivalent to the unit sphere S2n+1 of Cn+1.

Par des arguments topologiques introduits par Aubin–Bahri (1997), nous donnons quelques résultats d'existence pour le problème de la courbure scalaire de Webster sur les variétés CR de dimension 2n+1 localement conformément CR equivalent à la sphère unité S2n+1 de Cn+1.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2007.05.006

Hichem Chtioui  1

1 Département de mathématiques, faculté des sciences de Sfax, route Soukra, 3018 Sfax, Tunisia
Hichem Chtioui. The Webster scalar curvature problem on higher dimensional CR compact manifolds. Comptes Rendus. Mathématique, Volume 345 (2007) no. 1, pp. 11-13. doi: 10.1016/j.crma.2007.05.006
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[1] A. Ambrosetti; M. Badiale Homoclinics: Poincaré–Melnikov type results via a variational approach, Ann. Inst. H. Poincaré Anal. Non Linéaire, Volume 15 (1998), pp. 233-252

[2] T. Aubin; A. Bahri Méthode de topologie algebrique pour le probleme de la courbure scalaire prescrite, J. Math. Pures Appl., Volume 76 (1997), pp. 525-549

[3] T. Aubin; A. Bahri Une hypothese topologique pour le probleme de la courbure scalaire prescrite, J. Math. Pures Appl., Volume 76 (1997), pp. 843-850

[4] A. Bahri Critical Point at Infinity in Some Variational Problems, Pitman Res. Notes Math. Ser., vol. 182, Longman Sci. Tech., Harlow, 1989

[5] A. Bahri An invariant for Yamabe-type flows with applications to scalar curvature problems in high dimensions. A celebration of J.F. Nash Jr., Duke Math. J., Volume 81 (1996), pp. 323-466

[6] A. Bahri; J.M. Coron The scalar curvature problem on the standard three dimensional spheres, J. Funct. Anal., Volume 95 (1991), pp. 106-172

[7] M. Ben Ayed; Y. Chen; H. Chtioui; M. Hammami On the prescribed scalar curvature problem on 4-manifolds, Duke Math. J., Volume 84 (1996), pp. 633-677

[8] H. Chtioui, M. Ould Ahmedou, R. Yacoub, in preparation

[9] N. Gamara The prescribed scalar curvature on a 3-dimensional CR manifold, Adv. Nonlinear Stud., Volume 2 (2002), pp. 193-235

[10] N. Gamara The CR Yamabe conjecture, the case n=1, J. Eur. Math. Soc., Volume 3 (2001), pp. 105-137

[11] N. Gamara; R. Yacoub CR Yamabe conjecture, the conformally flat case, Pacific J. Math., Volume 201 (2001), pp. 121-175

[12] D. Jerismand; J.M. Lee The Yamabe problem on CR manifolds, J. Differential Geom., Volume 25 (1987), pp. 167-197

[13] D. Jerismand; J.M. Lee Extremals for the Sobolev inequality on the Heisenberg group and the CR Yamabe problem, J. Amer. Math. Soc., Volume 1 (1988), pp. 1-13

[14] D. Jerismand; J.M. Lee Intrinsic CR normal coordinates and the CR Yamabe problem, J. Differential Geom., Volume 29 (1989), pp. 303-343

[15] A. Malchiodi; F. Uguzzoni A perturbation result for the Webster scalar curvature problem on the CR sphere, J. Math. Pures Appl., Volume 81 (2002), pp. 983-997

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