[Métriques extrémales pour la Q′-courbure en dimension 3]
On construit des formes de contact à -courbure constante sur les variétés de Cauchy–Riemann de dimension 3 qui admettent une pseudo-forme de contact d'Einstein et satisfont certaines conditions naturelles de positivité. Ces formes sont obtenues en minimisant l'analogue en CR-géométrie de la II-fonctionelle en géométrie conforme. Cette construction repose sur deux étapes cruciales. On montre que le -opérateur peut être vu comme un opérateur pseudo-differentiel elliptique et on calcule les termes dominants du développement asymtotique de la forme de Green pour .
We construct contact forms with constant -curvature on compact three-dimensional CR manifolds that admit a pseudo-Einstein contact form and satisfy some natural positivity conditions. These contact forms are obtained by minimizing the CR analogue of the II-functional from conformal geometry. Two crucial steps are to show that the -operator can be regarded as an elliptic pseudodifferential operator and to compute the leading-order terms of the asymptotic expansion of the Green's function for .
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@article{CRMATH_2016__354_4_407_0,
author = {Case, Jeffrey S. and Hsiao, Chin-Yu and Yang, Paul},
title = {Extremal metrics for the {\protect\emph{Q}\protect\textsuperscript{'}-curvature} in three dimensions},
journal = {Comptes Rendus. Math\'ematique},
pages = {407--410},
publisher = {Elsevier},
volume = {354},
number = {4},
year = {2016},
doi = {10.1016/j.crma.2015.12.012},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2015.12.012/}
}
TY - JOUR AU - Case, Jeffrey S. AU - Hsiao, Chin-Yu AU - Yang, Paul TI - Extremal metrics for the Q′-curvature in three dimensions JO - Comptes Rendus. Mathématique PY - 2016 SP - 407 EP - 410 VL - 354 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2015.12.012/ DO - 10.1016/j.crma.2015.12.012 LA - en ID - CRMATH_2016__354_4_407_0 ER -
%0 Journal Article %A Case, Jeffrey S. %A Hsiao, Chin-Yu %A Yang, Paul %T Extremal metrics for the Q′-curvature in three dimensions %J Comptes Rendus. Mathématique %D 2016 %P 407-410 %V 354 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2015.12.012/ %R 10.1016/j.crma.2015.12.012 %G en %F CRMATH_2016__354_4_407_0
Case, Jeffrey S.; Hsiao, Chin-Yu; Yang, Paul. Extremal metrics for the Q′-curvature in three dimensions. Comptes Rendus. Mathématique, Tome 354 (2016) no. 4, pp. 407-410. doi : 10.1016/j.crma.2015.12.012. http://www.numdam.org/articles/10.1016/j.crma.2015.12.012/
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