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Hausdorff dimension and dendritic limit sets

Hausdorff dimension and dendritic limit sets
Hausdorff dimension and dendritic limit sets
Let Gamma be a singly degenerate closed surface group acting properly discontuously on hyperbolic 3-space, H3, such that H3/Gamma has positive injectivity radius. It is known that the limit set is a dendrite of Hausdorff dimension 2. We show that the cut-point set of the limit set has Hausdorff dimension strictly less than 2.
0025-5831
667-676
Bowditch, Brian H.
559a0b03-4ffd-49b0-aafe-4764e7de5143
Bowditch, Brian H.
559a0b03-4ffd-49b0-aafe-4764e7de5143

Bowditch, Brian H. (2005) Hausdorff dimension and dendritic limit sets. Mathematische Annalen, 332 (3), 667-676. (doi:10.1007/s00208-005-0647-1).

Record type: Article

Abstract

Let Gamma be a singly degenerate closed surface group acting properly discontuously on hyperbolic 3-space, H3, such that H3/Gamma has positive injectivity radius. It is known that the limit set is a dendrite of Hausdorff dimension 2. We show that the cut-point set of the limit set has Hausdorff dimension strictly less than 2.

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Published date: 2005

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Local EPrints ID: 29777
URI: http://eprints.soton.ac.uk/id/eprint/29777
ISSN: 0025-5831
PURE UUID: 7edec81a-ae08-4d2c-a44b-5d71b6be8bf7

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Date deposited: 11 May 2006
Last modified: 15 Jul 2019 19:08

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Author: Brian H. Bowditch

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