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.

Table of Contents

• Introduction
• Möbius coordinates
• Function spaces
• Elliptic operators
• Analysis on hyperbolic space
• Fredholm theorems
• Laplace operators
• Einstein metrics
• Bibliography