Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds
arXiv:math/0105046
Abstract
The main purpose of this monograph is to give an elementary and self-contained account of the existence of asymptotically hyperbolic Einstein metrics with prescribed conformal infinities sufficiently close to that of a given asymptotically hyperbolic Einstein metric with nonpositive curvature. The proof is based on an elementary derivation of sharp Fredholm theorems for self-adjoint geometric linear elliptic operators on asymptotically hyperbolic manifolds.
Latex; 83 + vi pages. Fixed an error in the proof of Lemma 3.7(b)