Dirichlet-to-Neumann Map for Poincaré - Einstein Metrics

Fang Wang
Princeton University

Room: UNIV 101

Feb 22, 2012 2:30 PM EST

I study the linearization of the Dirichlet-to-Neumann map for PE metrics on an arbitrary compact manifold with boundary. By fixing a suitable gauge, the linearized equation becomes elliptic. In this gauge, the linearization of DN map appears as the scattering matrix for an elliptic operator of 0-type, modified by some differential operator. Then I generalize a result of Graham for the case of standard hyperbolic metric on the ball.