Universal bounds for hyperbolic Dehn surgery

TL;DR

This paper provides quantitative bounds for hyperbolic Dehn surgery, offering universal limits on non-hyperbolic fillings and estimates on volume and geodesic length changes, advancing understanding of hyperbolic 3-manifolds.

Contribution

It introduces a quantitative version of Thurston's theorem and establishes universal bounds and estimates related to hyperbolic Dehn fillings.

Findings

Universal bounds on non-hyperbolic Dehn fillings

Estimates on volume changes during Dehn filling

Bounds on core geodesic length variations

Abstract

This 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.