Universal bounds for hyperbolic Dehn surgery
CD Hodgson, SP Kerckhoff
ANNALS OF MATHEMATICS | ANNALS MATHEMATICS, FINE HALL | Published : 2005
This paper gives a quantitative version of Thurston's hyperbolic Dehn surgery theorem. Applications include the first universal bounds on the number of nonhyperbolic Dehn fillings on a cusped hyperbolic 3-manifold, and estimates on the changes in volume and core geodesic length during hyperbolic Dehn filling. The proofs involve the construction of a family of hyperbolic conemanifold structures, using infinitesimal harmonic deformations and analysis of geometric limits.