[Des CR-invariants et la matrice de diffusion pour des variétés complexes avec CR-frontière]
Soit M une variété CR qui est aussi la frontière d'une variété complexe et compacte X. Il y a une métrique g de type Kähler–Einstein sur X telle que est une variété riemannienne complète. Nous étudions la matrice de diffusion sur et nous montrons que les résidus à certains points sont des opérateurs différentiels CR-covariants. Nous montrons aussi qu'on peut recuperer la courbure CR Q en utilisant la matrice de diffusion. Nos résultats sont les analogues des résultats de Graham–Zworski pour le cas réel et asymptotiquement hyperbolique.
Suppose that M is a CR manifold bounding a compact complex manifold X. The manifold X admits an approximate Kähler–Einstein metric g which makes the interior of X a complete Riemannian manifold. We identify certain residues of the scattering operator as CR-covariant differential operators and obtain the CR Q-curvature of M from the scattering operator as well. Our results are an analogue in CR-geometry of Graham and Zworski's result that certain residues of the scattering operator on a conformally compact manifold with a Poincaré–Einstein metric are natural, conformally covariant differential operators, and the Q-curvature of the conformal infinity can be recovered from the scattering operator.
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@article{CRMATH_2006__342_9_651_0,
author = {Hislop, Peter D. and Perry, Peter A. and Tang, Siu-Hung},
title = {CR-invariants and the scattering operator for complex manifolds with {CR-boundary}},
journal = {Comptes Rendus. Math\'ematique},
pages = {651--654},
publisher = {Elsevier},
volume = {342},
number = {9},
year = {2006},
doi = {10.1016/j.crma.2006.03.003},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2006.03.003/}
}
TY - JOUR AU - Hislop, Peter D. AU - Perry, Peter A. AU - Tang, Siu-Hung TI - CR-invariants and the scattering operator for complex manifolds with CR-boundary JO - Comptes Rendus. Mathématique PY - 2006 SP - 651 EP - 654 VL - 342 IS - 9 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2006.03.003/ DO - 10.1016/j.crma.2006.03.003 LA - en ID - CRMATH_2006__342_9_651_0 ER -
%0 Journal Article %A Hislop, Peter D. %A Perry, Peter A. %A Tang, Siu-Hung %T CR-invariants and the scattering operator for complex manifolds with CR-boundary %J Comptes Rendus. Mathématique %D 2006 %P 651-654 %V 342 %N 9 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2006.03.003/ %R 10.1016/j.crma.2006.03.003 %G en %F CRMATH_2006__342_9_651_0
Hislop, Peter D.; Perry, Peter A.; Tang, Siu-Hung. CR-invariants and the scattering operator for complex manifolds with CR-boundary. Comptes Rendus. Mathématique, Tome 342 (2006) no. 9, pp. 651-654. doi : 10.1016/j.crma.2006.03.003. http://www.numdam.org/articles/10.1016/j.crma.2006.03.003/
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