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Bounds on volume increase under Dehn drillingoperations

Published online by Cambridge University Press:  01 September 1998

M Bridgeman
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Abstract

In this paper we investigate how the volume of a hyperbolic manifold increases under the process of removing a curve, that is, Dehn drilling. If the curve we remove is a geodesic, we show that for a certain family of manifolds the volume increase is bounded above by $\pi \cdot l$ where $l$ is the length of the geodesic drilled. We further construct examples to show that there is no lower bound to the volume increase in terms of a monotonic unbounded function of length. In particular, this shows that volume increase is not bounded below linearly in length.

1991 Mathematics Subject Classification: primary 51M10, 51M20; secondary 51M25, 52C25.

Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 77 , Issue 2 , September 1998 , pp. 415 - 436
Copyright
London Mathematical Society 1998

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