Dehn Filling and Asymptotically Hyperbolic Einstein Manifolds
arXiv:math/0502491
Abstract
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.
30 pages, part of author's thesis from SUNY Stony Brook. Updated version, some slight corrections