[Un théorème d'uniformisation d'ordre 4 sur certaines variétés de dimension 4 à large Q-courbure totale]
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 , 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.
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@article{CRMATH_2005__340_5_341_0,
author = {Djadli, Zindine and Malchiodi, Andrea},
title = {A fourth order uniformization theorem on some four manifolds with large total {\protect\emph{Q}-curvature}},
journal = {Comptes Rendus. Math\'ematique},
pages = {341--346},
publisher = {Elsevier},
volume = {340},
number = {5},
year = {2005},
doi = {10.1016/j.crma.2005.01.013},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2005.01.013/}
}
TY - JOUR AU - Djadli, Zindine AU - Malchiodi, Andrea TI - A fourth order uniformization theorem on some four manifolds with large total Q-curvature JO - Comptes Rendus. Mathématique PY - 2005 SP - 341 EP - 346 VL - 340 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2005.01.013/ DO - 10.1016/j.crma.2005.01.013 LA - en ID - CRMATH_2005__340_5_341_0 ER -
%0 Journal Article %A Djadli, Zindine %A Malchiodi, Andrea %T A fourth order uniformization theorem on some four manifolds with large total Q-curvature %J Comptes Rendus. Mathématique %D 2005 %P 341-346 %V 340 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2005.01.013/ %R 10.1016/j.crma.2005.01.013 %G en %F CRMATH_2005__340_5_341_0
Djadli, Zindine; Malchiodi, Andrea. A fourth order uniformization theorem on some four manifolds with large total Q-curvature. Comptes Rendus. Mathématique, Tome 340 (2005) no. 5, pp. 341-346. doi : 10.1016/j.crma.2005.01.013. http://www.numdam.org/articles/10.1016/j.crma.2005.01.013/
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