2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63934This paper gives a quantitative version of Thurston's hyperbolic Dehn surgery theorem. Applications include the first universal bounds on the number of non-hyperbolic 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.45 pages, 2 figuresGeometric TopologyDifferential Geometry57M50, 57N10, 57M25, 53C25text