Compactness of solutions to the Yamabe problem

YanYan Li; Lei Zhang

doi:10.1016/j.crma.2004.02.018

Partial Differential Equations

Compactness of solutions to the Yamabe problem

Presented by: Haïm Brezis

YanYan Li ¹; Lei Zhang 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

Comptes Rendus. Mathématique, Volume 338 (2004) no. 9, pp. 693-695.

Abstract
Résumé

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.

Received: 2004-02-24
Accepted: 2004-02-24
Published online: 2004-03-27

DOI: 10.1016/j.crma.2004.02.018

Author's affiliations:

YanYan Li ¹; Lei Zhang 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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     title = {Compactness of solutions to the {Yamabe} problem},
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     pages = {693--695},
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     doi = {10.1016/j.crma.2004.02.018},
     language = {en},
}

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YanYan Li; Lei Zhang. Compactness of solutions to the Yamabe problem. Comptes Rendus. Mathématique, Volume 338 (2004) no. 9, pp. 693-695. doi : 10.1016/j.crma.2004.02.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.02.018/

References
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