Dehn filling and asymptotically hyperbolic Einstein manifolds

In this article, we extend Anderson's higher dimensional Dehn filling construction to a large class of infinite-volume hyperbolic manifolds. This gives an infinite family of topologically distinct asymptotically hyperbolic Einstein manifolds with the same conformal infinity. The construction involves finding a sequence of approximate solutions to the Einstein equations and then perturbing them to exact ones.

2010 Mathematics Subject Classification

53Cxx

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Published 1 January 2006