Linear volume bounds for drilling and filling

TL;DR

This paper establishes uniform linear bounds on how the volume of finite volume hyperbolic 3-manifolds changes when performing drilling and filling operations, providing new quantitative insights into their geometric behavior.

Contribution

It introduces the first uniform linear volume bounds for drilling and filling in hyperbolic 3-manifolds, advancing understanding of their geometric transformations.

Findings

Proves linear bounds on volume variation during drilling.

Establishes linear bounds on volume change during filling.

Provides a quantitative framework for hyperbolic 3-manifold modifications.

Abstract

We prove uniform linear bounds on the volume variation under drilling and filling operations on finite volume hyperbolic 3-manifolds.