English

Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds

Differential Geometry 2007-05-23 v5 Analysis of PDEs

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.

Keywords

Cite

@article{arxiv.math/0105046,
  title  = {Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds},
  author = {John M. Lee},
  journal= {arXiv preprint arXiv:math/0105046},
  year   = {2007}
}

Comments

Latex; 83 + vi pages. Fixed an error in the proof of Lemma 3.7(b)

R2 v1 2026-07-22T16:38:35.721Z