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Astérisque - Titles - 322 (2008) 23-38

Titles < 2008 < 322

Géométrie différentielle, physique mathématique, mathématiques et société (II)
Volume en l'honneur de Jean Pierre Bourguignon

Oussama Hijazi (éditeur)
Astérisque 322 (2008), xvi+256 pages
Buy the book
Presentation, Summary

The Q-curvature Equation in Conformal Geometry
Sun-Yung Alice Chang, Paul C. Yang
Astérisque 322 (2008), 23-38

Résumé :
L'équation de Q-courbure en géométrie conforme
Dans cet article nous examinons certains résultats analytiques autour de l'équation de Q-courbure d'ordre maximal en géométrie conforme. La Q-courbure est la généralisation naturelle de la courbure de Gauss aux variétés de dimension paire. Sa proximité avec le pfaffien (l'intégrande de la formule de Gauss-Bonnet) nous fournit une relation directe entre géométrie et topologie.

Mots-clefs : Q-courbure, compactification, structure de Poincaré-Einstein, volume renormalisé

Abstract:
In this paper we survey some analytic results concerned with the top order Q-curvature equation in conformal geometry. Q-curvature is the natural generalization of the Gauss curvature to even dimensional manifolds. Its close relation to the Pfaffian, the integrand in the Gauss-Bonnet formula, provides a direct relation between curvature and topology.

Keywords: Q-curvature, compactification, Poincaré-Einstein structure, renormalized volume

Class. math. : 53A30, 58J05, 35J60


ISSN : 0303-1179
Publié avec le concours de : Centre National de la Recherche Scientifique

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