Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds

Presents an account of the existence of asymptotically hyperbolic Einstein metrics with prescribed conformal infinities which is sufficiently close to that of a given asymptotically hyperbolic Einstein metric with non positive curvature. This book features the proof that is based on a derivation of Fredholm theorems.

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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 non positive curvature. The proof is based on an elementary derivation of sharp Fredholm theorems for self-adjoint geometric linear elliptic operators on asymptotically hyperbolic manifolds.