Hausdorff dimension and limits of Kleinian groups
Hausdorff dimension and limits of Kleinian groups
Richard D. Canary1 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:
1Research 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.