3/22/2005

Dirichlet-to-Neumann map for Poincaré-Einstein metrics

This talk will describe an analogue of a Dirichlet to Neumann map for Poincar\'e-Einstein metrics, also known as asymptotically hyperbolic or conformally compact Einstein metrics. An explicit identification of the linearization of the map at the sphere will be given for even interior dimensions, together with applications to the structure of the map near the sphere and to a different proof of the positive frequency conjecture of LeBrun which was resolved by Biquard.