Dirichlet-to-Neumann map for Poincaré–Einstein metrics in even dimensions
Copyright policy )Dirichlet-to-Neumann map for Poincaré–Einstein metrics in even dimensions
We study the linearization of the Dirichlet-to-Neumann map for Poincar��-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.
40 pages
- Shanghai Jiao Tong University China (People's Republic of)
Mathematics - Differential Geometry, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), Spectral problems; spectral geometry; scattering theory on manifolds, Dirichlet-to-Neumann map, FOS: Mathematics, Poincaré-Einstein metrics, Boundary value problems on manifolds, 58J32, Analysis of PDEs (math.AP)
Mathematics - Differential Geometry, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), Spectral problems; spectral geometry; scattering theory on manifolds, Dirichlet-to-Neumann map, FOS: Mathematics, Poincaré-Einstein metrics, Boundary value problems on manifolds, 58J32, Analysis of PDEs (math.AP)
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