Dirichlet-to-Neumann Map for Poincar\'e-Einstein Metrics in Even Dimensions
Differential Geometry
2009-05-18 v1 Analysis of PDEs
Abstract
We study the linearization of the Dirichlet-to-Neumann map for Poincar\'e-Einstein metrics in even dimensions on an arbitrary compact manifold with boundary. By fixing a suitable gauge, we make the linearized Einstein equation elliptic. In this gauge the linearization of the Dirichlet-to-Neumann map appears as the scattering matrix for an elliptic operator of 0-type, modified by some differential operators. We study the scattering matrix by using the 0-calculus and generalize a result of Graham for the case of the standard hyperbolic metric on a ball.
Keywords
Cite
@article{arxiv.0905.2457,
title = {Dirichlet-to-Neumann Map for Poincar\'e-Einstein Metrics in Even Dimensions},
author = {Fang Wang},
journal= {arXiv preprint arXiv:0905.2457},
year = {2009}
}
Comments
40 pages