Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds

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)

References in corpus (1)

• Boundary regularity, uniqueness and non-uniqueness for AH Einstein metrics on 4-manifolds

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• Maskit combinations of Poincare-Einstein metrics
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