Geodesic
Partial Differential Equations
Compactness of solutions to the Yamabe problem
[Compacité des solutions du problème de Yamabe]

Présenté par : Haïm Brezis

Li, YanYan1 ; Zhang, Lei2
1 Department of Mathematics, Rutgers University, 110 Frelinghuysen Rd., Piscataway, NJ 08854, USA
2 Department of Mathematics, Texas A&M University, 3368 TAMU, College Station, TX 77843-3368, USA
Comptes Rendus. Mathématique, Tome 338 (2004) no. 9, pp. 693-695.

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We establish compactness of solutions to the Yamabe problem on any smooth compact connected Riemannian manifold (not conformally diffeomorphic to standard spheres) of dimension n⩽7 as well as on any manifold of dimension n⩾8 under some additional hypothesis.

On établit la compacité des solutions du problème de Yamabe sur toute variété riemannienne, régulière compacte connexe (non conformément équivalente à la sphère standard) de dimension n⩽7. Le même résultat est valable en dimension n⩾8 sous une hypothèse supplémentaire.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2004.02.018

Li, YanYan 1 ; Zhang, Lei 2

1 Department of Mathematics, Rutgers University, 110 Frelinghuysen Rd., Piscataway, NJ 08854, USA
2 Department of Mathematics, Texas A&M University, 3368 TAMU, College Station, TX 77843-3368, USA 
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Li, YanYan; Zhang, Lei. Compactness of solutions to the Yamabe problem. Comptes Rendus. Mathématique, Tome 338 (2004) no. 9, pp. 693-695. doi : 10.1016/j.crma.2004.02.018. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2004.02.018/

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