Conformal Dirichlet-Neumann Maps and Poincaré-Einstein Manifolds

Details Conformal Dirichlet-Neumann Maps and Poincaré-Einstein Manifolds Conformal Dirichlet-Neumann Maps and Poincaré-Einstein Manifolds

2007-10-13

arxiv.org/abs/0710.2585v2

SIGMA 3 (2007), 100, 21 pages

Mathematics

Differential Geometry

This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in

Scientific paper

10.3842/SIGMA.2007.100

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.

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