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Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds

John M. Lee University of Washington, Seattle, WA
Available Formats:
Electronic ISBN: 978-1-4704-0468-0
Product Code: MEMO/183/864.E
List Price: $60.00 MAA Member Price:$54.00
AMS Member Price: $36.00 Click above image for expanded view Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds John M. Lee University of Washington, Seattle, WA Available Formats:  Electronic ISBN: 978-1-4704-0468-0 Product Code: MEMO/183/864.E  List Price:$60.00 MAA Member Price: $54.00 AMS Member Price:$36.00
• Book Details

Memoirs of the American Mathematical Society
Volume: 1832006; 83 pp
MSC: Primary 53; Secondary 58;

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

• Chapters
• 1. Introduction
• 2. Möbius coordinates
• 3. Function spaces
• 4. Elliptic operators
• 5. Analysis on Hyperbolic space
• 6. Fredholm theorems
• 7. Laplace operators
• 8. Einstein metrics
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Volume: 1832006; 83 pp
MSC: Primary 53; Secondary 58;

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.

• Chapters
• 1. Introduction
• 2. Möbius coordinates
• 3. Function spaces
• 4. Elliptic operators
• 5. Analysis on Hyperbolic space
• 6. Fredholm theorems
• 7. Laplace operators
• 8. Einstein metrics
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