Prescribing the Webster scalar curvature on <i>CR</i> spheres

Ridha Yacoub

doi:10.1016/j.crma.2011.11.007

Differential Topology/Calculus of Variations

Prescribing the Webster scalar curvature on CR spheres
[Préscription de la courbure scalaire de Webster sur la sphère CR]

Présenté par : Haïm Brézis

Ridha Yacoub ¹

¹ Département de mathématique-informatique, I.P.E.I.M., rue Ibn Al Jazzar, 5019 Monastir, Tunisia

Comptes Rendus. Mathématique, Volume 349 (2011) no. 23-24, pp. 1277-1280.

Résumé
Abstract

Dans cette Note, on donne deux nouveaux résultats perturbatifs pour préscrire la courbure scalaire de Webster sur la sphère de dimension $(2 n + 1)$ munie de sa structure CR standard. Le premier résultat généralise celui obtenu par A. Malchiodi et F. Uguzzoni (2002) dans [9].

In this Note, we give two new perturbative results for prescribing the Webster scalar curvature on the $(2 n + 1)$ -dimensional sphere endowed with its standard CR structure. The first result generalizes the one obtained by A. Malchiodi and F. Uguzzoni (2002) in [9].

Reçu le : 2011-09-20
Accepté le : 2011-11-09
Publié le : 2011-11-25

DOI : 10.1016/j.crma.2011.11.007

Affiliations des auteurs :

Ridha Yacoub ¹

¹ Département de mathématique-informatique, I.P.E.I.M., rue Ibn Al Jazzar, 5019 Monastir, Tunisia

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     author = {Ridha Yacoub},
     title = {Prescribing the {Webster} scalar curvature on {\protect\emph{CR}} spheres},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1277--1280},
     publisher = {Elsevier},
     volume = {349},
     number = {23-24},
     year = {2011},
     doi = {10.1016/j.crma.2011.11.007},
     language = {en},
}

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Ridha Yacoub. Prescribing the Webster scalar curvature on CR spheres. Comptes Rendus. Mathématique, Volume 349 (2011) no. 23-24, pp. 1277-1280. doi : 10.1016/j.crma.2011.11.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.11.007/

Bibliographie
Cité par

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[2] A. Bahri; J.-M. Coron The scalar curvature problem on the standard three-dimensional sphere, J. Funct. Anal., Volume 95 (1991) no. 1, pp. 106-172

[3] H. Chtioui; M.O. Ahmedou; R. Yacoub Topological methods for the prescribed Webster scalar curvature problem on CR manifolds, Diff. Geom. Appl., Volume 28 (2010), pp. 264-281

[4] H. Chtioui, M.O. Ahmedou, R. Yacoub, Existence and multiplicity results for the prescribed Webster scalar curvature problem on three CR manifolds, J. Geom. Anal., , in press. | DOI

[5] V. Felli; F. Uguzzoni Some existence results for the Webster scalar curvature problem in presence of symmetry, Annali di Matematica, Volume 183 (2004), pp. 469-493

[6] N. Gamara; R. Yacoub CR Yamabe conjecture – the conformally flat case, Pac. J. Math., Volume 201 (2001) no. 1, pp. 121-175

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

[8] A. Malchiodi The scalar curvature problem on $S^{n}$ : an approach via Morse theory, Calc. Var. PDEs, Volume 14 (2002), pp. 429-445

[9] 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

[10] R. Schoen; D. Zhang Prescribed scalar curvature problem on the n-sphere, Calc. Var. PDEs, Volume 4 (1996), pp. 1-25

[11] R. Yacoub On the scalar curvature equations in high dimension, Adv. Nonlin. Stud., Volume 2 (2002) no. 4, pp. 373-393

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