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Scattering matrix in conformal geometry
This paper describes the connection between scattering matrices on conformally compact asymptotically Einstein manifolds and conformally invariant objects on their boundaries at infinity. TheExpand
The Ambient Metric
Chapter 1. Introduction 1 Chapter 2. Ambient Metrics 9 Chapter 3. Formal Theory 17 Chapter 4. Poincar'e Metrics 42 Chapter 5. Self-dual Poincar'e Metrics 50 Chapter 6. Conformal Curvature Tensors 56Expand
Volume and Area Renormalizations for Conformally Compact Einstein Metrics
Let $X$ be the interior of a compact manifold $\overline X$ of dimension $n+1$ with boundary $M=\partial X$, and $g_+$ be a conformally compact metric on $X$, namely $\overline g\equiv r^2g_+$Expand
Einstein metrics with prescribed conformal infinity on the ball
In this paper we study a boundary problem for Einstein metrics. Let A4 be the interior of a compact (n + l)-dimensional manifold-with-boundary I@, and g a Riemannian metric on M. If 2 is a metric onExpand
Conformal anomaly of submanifold observables in AdS/CFT correspondence☆
We analyze the conformal invariance of submanifold observables associated with k-branes in the AdS/CFT correspondence. For odd k, the resulting obsrvables are conformally invariant, and for even k,Expand
Smooth solutions of degenerate Laplacians on strictly pseudoconvex domains
On considere la caracterisation des solutions lisses globales de Δφu=0 sur un domaine general strictement pseudoconvexe, ou Δφ est le laplacien pour la metrique avec forme de Kakler (i/2) ∂ log (−1/φ)
$Q$-Curvature and Poincaré Metrics
This article presents a new definition of Branson's Q-curvature in even-dimensional conformal geometry. We derive the Q-curvature as a coefficient in the asymptotic expansion of the formal solutionExpand
CR invariant powers of the sub-Laplacian
Abstract CR invariant differential operators on densities with leading part a power of the sub-Laplacian are derived. One family of such operators is constructed from the ‘‘conformally invariantExpand