Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 3 (2007), 100, 21 pages      arXiv:0710.2585      http://dx.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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