Communications in Analysis and Geometry
Volume 14 (2006)
Dehn filling and asymptotically hyperbolic Einstein manifolds
Pages: 725 – 764
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