Conformal Dirichlet-Neumann Maps and Poincaré-Einstein Manifolds

Abstract

A conformal description of Poincare-Einstein manifolds is developed: these structures are seen to be a special case of a natural weakening of the Einstein condition termed an almost Einstein structure. This is used for two purposes: to shed light on the relationship between the scattering construction of Graham-Zworski and the higher order conformal Dirichlet-Neumann maps of Branson and the author; to sketch a new construction of non-local (Dirichlet-to-Neumann type) conformal operators between tensor bundles.

This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

References in corpus (3)

• Almost conformally Einstein manifolds and obstructions
• Standard Tractors and the Conformal Ambient Metric Construction
• Curved Casimir Operators and the BGG Machinery

Cited by in corpus (1)

• Almost Einstein and Poincare-Einstein manifolds in Riemannian signature