Comptes Rendus
no. 7
Partial Differential Equations
A Kazdan–Warner type identity for the σk curvature
[Une identité de type Kazdan–Warner pour la σk-courbure]

Présenté par : Haïm Brezis

Zheng-Chao Han1
1 Department of Mathematics, Rutgers University, 110, Frelinghuysen Road, Piscataway, NJ 08854, USA
Comptes Rendus. Mathématique, Volume 342 (2006) no. 7, pp. 475-478.

Nous prouvons une identité de type Kazdan–Warner reliant la σk-courbure et un champ de vecteurs conforme sur une variété compacte. Notre méthode permet aussi de fournir une preuve unifiée pour les conditions nécessaires dans le problème de Christoffel–Minkowski.

We prove a Kazdan–Warner type identity involving the σk curvature and a conformal Killing vector field on a compact manifold. Our method also works to provide a unified proof for the necessary conditions in the Christoffel–Minkowski problem.

Reçu le :
Publié le :
DOI : 10.1016/j.crma.2006.01.023

Zheng-Chao Han 1

1 Department of Mathematics, Rutgers University, 110, Frelinghuysen Road, Piscataway, NJ 08854, USA 
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Zheng-Chao Han. A Kazdan–Warner type identity for the $ {\sigma }_{k}$ curvature. Comptes Rendus. Mathématique, Volume 342 (2006) no. 7, pp. 475-478. doi : 10.1016/j.crma.2006.01.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.01.023/

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