Conformal Dirichlet–Neumann Maps and Poincaré–Einstein Manifolds

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.