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Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds

John M. Lee
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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.

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John M. Lee. 2006-07-27. Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds. https://arxiv.org/abs/math/0105046

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