Universal bounds for hyperbolic Dehn surgery


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 cone-manifold structures, using infinitesimal harmonic deformations and analysis of geometric limits.


Craig Hodgson

Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia

Steven P. Kerckhoff

Department of Mathematics, Stanford University, Stanford, CA 94305, United States