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Opérateurs Géométriques, Invariants Conformes et Variétés Asymptotiquement Hyperboliques
Zindine Djadli, Université Grenoble I, St. Martin d'Heres, France, Colin Guillarmou, Université de Nice-Sophia Antipolis, France, and Marc Herzlich, Université Montpellier II, France
A publication of the Société Mathématique de France.
Panoramas et Synthèses
2008; 171 pp; softcover
Number: 26
ISBN-10: 2-85629-260-7
ISBN-13: 978-2-85629-260-0
List Price: US$55
Member Price: US$44
Order Code: PASY/26
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In 1985, Fefferman and Graham initiated an ambitious program of study of conformal geometry known as the "ambient metric" method. This program has developed tremendously in the last few years, leading to the definition of a number of new invariants: Graham-Jenne-Mason-Sparling (GJMS) operators generalizing the Yamabe and Paneitz operators, Branson \(Q\)-curvatures ... and to remarkable applications to conformally flat manifolds of dimension \(4\) and nonnegative Euler characteristic, or to conformally invariant pinching theorems. An essential role is played in the theory by asymptotically hyperbolic Einstein metrics (or Poincaré-Einstein metrics) associated to a conformal class.

This book is devoted to a presentation of the theory together with a description of the latest developments. It should be accessible to all readers having a basic knowledge of Riemannian geometry.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.


Graduate students and research mathematicians interested in geometric operators, conformal invariants and asymptotically hyperbolic manifolds.

Table of Contents

  • Introduction
  • Métriques AHE et ambiantes
  • Premières applications
  • Intégrales renormalisées
  • Théorie de la diffusion
  • Laplaciens conformes et \(Q\)-courbure
  • Fonctionnelle log-déterminant, \(Q\)-courbure et applications en dimension 4
  • Variétés riemanniennes mesurées
  • La métrique ambiante et le fibré de Cartan
  • Déterminants des opérateurs GJMS et fonctions Zêta
  • Bibliographie
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