Boundary regularity, uniqueness and non-uniqueness for AH Einstein metrics on 4-manifolds |
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Authors: | Michael T Anderson |
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Institution: | Department of Mathematics, SUNY at Stony Brook, Stony Brook, NY 11794-3651, USA |
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Abstract: | This paper studies several aspects of asymptotically hyperbolic (AH) Einstein metrics, mostly on 4-manifolds. We prove boundary regularity (at infinity) for such metrics and establish uniqueness under natural conditions on the boundary data. By examination of explicit black hole metrics, it is shown that neither uniqueness nor finiteness holds in general for AH Einstein metrics with a prescribed conformal infinity. We then describe natural conditions which are sufficient to ensure finiteness. |
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Keywords: | primary 53C25 58J60 secondary 58D17 |
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