[La conjecture de Hebey–Vaugon II]
Dans cette Note, on considère les cas restants de la conjecture de Hebey–Vaugon. En admettant la théorème de la masse positive, on donne une réponse positive à cette conjecture.
In this Note, we consider the remaining cases of Hebey–Vaugon conjecture. Assuming the positive mass theorem, we give a positive answer to this conjecture.
Accepté le :
Publié le :
Farid Madani 1
@article{CRMATH_2012__350_17-18_849_0, author = {Farid Madani}, title = {Hebey{\textendash}Vaugon conjecture {II}}, journal = {Comptes Rendus. Math\'ematique}, pages = {849--852}, publisher = {Elsevier}, volume = {350}, number = {17-18}, year = {2012}, doi = {10.1016/j.crma.2012.10.004}, language = {en}, }
Farid Madani. Hebey–Vaugon conjecture II. Comptes Rendus. Mathématique, Volume 350 (2012) no. 17-18, pp. 849-852. doi : 10.1016/j.crma.2012.10.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.10.004/
[1] Équations différentielles non linéaires et problème de Yamabe, J. Math. Pures et Appl., Volume 55 (1976), pp. 269-296
[2] Sur quelques problèmes de courbure scalaire, J. Funct. Anal., Volume 240 (2006), pp. 269-289
[3] Courbure scalaire prescrite pour des variétés non conformément difféomorphes à la sphère, C. R. Acad. Sci. Paris, Ser. I, Volume 316 (1993) no. 3, pp. 281-282
[4] Le problème de Yamabe équivariant, Bull. Sci. Math., Volume 117 (1993), pp. 241-286
[5] A compactness theorem for the Yamabe problem, J. Diff. Geom., Volume 81 (2009), pp. 143-196
[6] The Yamabe problem, Bull. Amer. Math. Soc., Volume 17 (1987), pp. 37-91
[7] Sur les transformations conformes dʼune variété riemannienne compacte, C. R. Acad. Sci. Paris, Volume 259 (1964)
[8] F. Madani, Le problème de Yamabe equivariant et la conjecture de Hebey–Vaugon, Ph.D. thesis, Université Pierre et Marie Curie, 2009.
[9] Equivariant Yamabe problem and Hebey–Vaugon conjecture, J. Func. Anal., Volume 258 (2010), pp. 241-254
[10] Blow-up examples for the Yamabe problem, Calc. Var., Volume 36 (2009), pp. 377-397
[11] Conformal deformation of a Riemannian metric to constant scalar curvature, J. Differ. Geom., Volume 20 (1984), pp. 479-495
[12] Remarks concerning the conformal deformation of Riemannian structures on compact manifolds, Ann. Scuola Norm. Sup. Pisa, Volume 22 (1968), pp. 265-274
[13] On a deformation of Riemannian structures on compact manifolds, Osaka Math. J., Volume 12 (1960), pp. 21-37
- Equivariant CR Yamabe problem, Annali di Matematica Pura ed Applicata. Serie Quarta, Volume 204 (2025) no. 1, pp. 289-306 | DOI:10.1007/s10231-024-01484-6 | Zbl:7985716
- Equivariant solutions to the optimal partition problem for the prescribed
-curvature equation, The Journal of Geometric Analysis, Volume 34 (2024) no. 4, p. 51 (Id/No 111) | DOI:10.1007/s12220-024-01554-4 | Zbl:1535.53038 - Equivariant Yamabe problem with boundary, Calculus of Variations and Partial Differential Equations, Volume 61 (2022) no. 1, p. 37 (Id/No 38) | DOI:10.1007/s00526-021-02154-8 | Zbl:1503.53064
- Isoparametric functions and nodal solutions of the Yamabe equation, Annals of Global Analysis and Geometry, Volume 56 (2019) no. 2, pp. 203-219 | DOI:10.1007/s10455-019-09664-x | Zbl:1467.53045
- The equivariant second Yamabe constant, The Journal of Geometric Analysis, Volume 28 (2018) no. 4, pp. 3747-3774 | DOI:10.1007/s12220-017-9978-x | Zbl:1407.53035
- About the mass of certain second order elliptic operators, Advances in Mathematics, Volume 294 (2016), pp. 596-633 | DOI:10.1016/j.aim.2016.03.008 | Zbl:1338.58012
- A detailed proof of a theorem of Aubin, The Journal of Geometric Analysis, Volume 26 (2016) no. 1, pp. 231-251 | DOI:10.1007/s12220-014-9547-5 | Zbl:1338.53033
Cité par 7 documents. Sources : zbMATH
Commentaires - Politique