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SIGMA 3 (2007), 100, 21 pages arXiv:0710.2585
https://doi.org/10.3842/SIGMA.2007.100
Contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson
Conformal Dirichlet-Neumann Maps and Poincaré-Einstein Manifolds
A. Rod Gover
Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland 1,
New Zealand
Received October 07, 2007; Published online October 21, 2007
Abstract
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.
Key words:
conformal differential geometry; Dirichlet-to-Neumann maps.
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