Conformal Dirichlet-Neumann Maps and Poincaré-Einstein Manifolds - Gover, A.R. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
A conformal description of Poincaré-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.