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Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds
John M. Lee, University of Washington, Seattle, WA

Memoirs of the American Mathematical Society
2006; 83 pp; softcover
Volume: 183
ISBN-10: 0-8218-3915-2
ISBN-13: 978-0-8218-3915-7
List Price: US$60
Individual Members: US$36
Institutional Members: US$48
Order Code: MEMO/183/864
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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
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