Communications in Analysis and Geometry

Volume 14 (2006)

Number 4

Dehn filling and asymptotically hyperbolic Einstein manifolds

Pages: 725 – 764

DOI: http://dx.doi.org/10.4310/CAG.2006.v14.n4.a6

Author

Gordon Craig

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.

2010 Mathematics Subject Classification

53Cxx

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