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Hausdorff dimension and dendritic limit sets

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Abstract

Let Γ be a singly degenerate closed surface group acting properly discontinuously on hyperbolic 3-space, H3, such that H3/Γ 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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  1. Faculty of Mathematical Studies, University of Southampton, Highfield, Southampton, SO17 1BJ, Great Britain

    Brian H. Bowditch

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  1. Brian H. Bowditch
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Bowditch, B. Hausdorff dimension and dendritic limit sets. Math. Ann. 332, 667–676 (2005). https://doi.org/10.1007/s00208-005-0647-1

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  • DOI: https://doi.org/10.1007/s00208-005-0647-1

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