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Scattering matrix in conformal geometry

- C. R. Graham, M. Zworski
- Physics, Mathematics
- 14 September 2001

This paper describes the connection between scattering matrices on conformally compact asymptotically Einstein manifolds and conformally invariant objects on their boundaries at infinity. The… Expand

The Ambient Metric

- C. Fefferman, C. R. Graham
- Mathematics
- 4 October 2007

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 56… Expand

Volume and Area Renormalizations for Conformally Compact Einstein Metrics

- C. R. Graham
- Mathematics, Physics
- 8 September 1999

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

- C. R. Graham, John M. Lee
- Mathematics
- 1 June 1991

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 on… Expand

Conformally Invariant Powers of the Laplacian, I: Existence

- C. R. Graham, Ralph Jenne, L. Mason, G. Sparling
- Mathematics
- 1 December 1992

Conformal anomaly of submanifold observables in AdS/CFT correspondence☆

- C. R. Graham, E. Witten
- Physics
- 6 January 1999

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

- C. R. Graham, John M. Lee
- Mathematics
- 1 December 1988

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

- C. Fefferman, C. R. Graham
- Mathematics
- 24 October 2001

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 solution… Expand

CR invariant powers of the sub-Laplacian

- A. Gover, C. R. Graham
- Mathematics
- 9 January 2003

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 invariant… Expand

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