Conformal Dirichlet-Neumann maps and Poincaré-Einstein manifolds
SIGMA, Symmetry Integrability Geom. Methods Appl. 3, Paper 100, 21 p., electronic only (2007)
Summary: 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.
Mathematics Subject Classification
58J40, 53A30, 58J32
conformal differential geometry, Dirichlet-to-Neumann maps