Hausdorff dimension and limits of Kleinian groups
# Hausdorff dimension and limits of Kleinian groups

### Richard D. Canary^{1} and Edward C. Taylor

### Department of Mathematics, University of Michigan, Ann Arbor, MI 48109

## Abstract

In this paper we prove that if M is a compact, hyperbolizable
3-manifold, which is not a handlebody,
then the Hausdorff dimension of the limit set is continuous
in the strong topology on the space of marked
hyperbolic 3-manifolds homotopy equivalent to M.
We similarly observe that for any compact hyperbolizable 3-manifold
M (including a handlebody), the bottom of the spectrum
of the Laplacian gives a continuous function in the strong topology
on the space of
topologically tame hyperbolic 3-manifolds homotopy equivalent to M.

### Footnotes:

^{1}Research supported
in part by the National Science Foundation and a fellowship from the
Sloan Foundation

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On 27 Nov 1999, 14:13.