Memoirs of the American Mathematical Society

1 total work

Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds

by John M Lee

Published 15 August 2006

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.