Comptes Rendus
no. 5
Partial Differential Equations
A fourth order uniformization theorem on some four manifolds with large total Q-curvature
[Un théorème d'uniformisation d'ordre 4 sur certaines variétés de dimension 4 à large Q-courbure totale]

Présenté par : Haïm Brezis

Zindine Djadli1 ; Andrea Malchiodi2
1 Université de Cergy-Pontoise, département de mathématiques, site de Saint-Martin, 2, avenue Adolphe-Chauvin, 95302 Cergy-Pontoise cedex, France
2 SISSA, via Beirut 2-4, 34014 Trieste, Italy
Comptes Rendus. Mathématique, Volume 340 (2005) no. 5, pp. 341-346.

Etant donnée une variété riemannienne compacte de dimension 4, on étudie l'existence d'une métrique conforme, pour laquelle la Q-courbure, associée à un opérateur d'ordre 4 (l'opérateur de Paneitz) est constante. En utilisant un argument topologique, nous obtenons des résultats nouveaux dans des cas auparavant encore ouverts.

Given a four-dimensional manifold (M,g), we study the existence of a conformal metric for which the Q-curvature, associated to a conformally invariant fourth-order operator (the Paneitz operator), is constant. Using a topological argument, we obtain a new result in cases which were still open.

Reçu le :
Publié le :
DOI : 10.1016/j.crma.2005.01.013
Zindine Djadli 1 ; Andrea Malchiodi 2

1 Université de Cergy-Pontoise, département de mathématiques, site de Saint-Martin, 2, avenue Adolphe-Chauvin, 95302 Cergy-Pontoise cedex, France
2 SISSA, via Beirut 2-4, 34014 Trieste, Italy 
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     pages = {341--346},
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     language = {en},
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Zindine Djadli; Andrea Malchiodi. A fourth order uniformization theorem on some four manifolds with large total Q-curvature. Comptes Rendus. Mathématique, Volume 340 (2005) no. 5, pp. 341-346. doi : 10.1016/j.crma.2005.01.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.01.013/

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