Year: 1995
Type: preprint
Abstract: In this paper we investigate how the volume of hyperbolic manifolds increases under the process of removing a curve, that is, Dehn drilling. If the curve we remove is a geodesic we are able to show that for a certain family of manifolds the volume increase is bounded above by $π\cdot l$ where $l$ is the length of the geodesic drilled. Also we construct examples to show that there is no lower bound to the volume increase in terms of a linear function of a positive power of length and in particular volume increase is not bounded linearly in length.
Source: arXiv (Cornell University)
Author: Bridgeman, Martin
Institution: Loyola University New Orleans
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2951478453