Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds
نویسنده
چکیده
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. Received by the editor February 16, 2004. 2000 Mathematics Subject Classification. Primary 53C25; Secondary 58J05, 58J60.
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