Conformal Dirichlet-Neumann Maps and Poincar\'e-Einstein Manifolds
Differential Geometry
2008-04-25 v2 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.0710.2585,
title = {Conformal Dirichlet-Neumann Maps and Poincar\'e-Einstein Manifolds},
author = {A. Rod Gover},
journal= {arXiv preprint arXiv:0710.2585},
year = {2008}
}
Comments
This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/