Alan Pinoy: Elliptic operators on asymptotically hyperbolic manifolds, and an application to the deformation of Poincaré-Einstein metrics

The study of elliptic operators on asymptotically hyperbolic manifolds is much difficult, due to the non-compactness of such manifolds. In this talk, I will present an elliptic theory developed by John M. Lee in the monograph Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds, which allows one to cover a large class of elliptic operators of geometric nature. As a direct application, I will explain a result of Lee, which shows that we can deform a given Poincaré-Einstein metric on a conformally compact manifolds by prescribing its conformal infinity.