Hausdorff dimension and dendritic limits sets

Brian H. Bowditch

Let \Gamma be a singly degenerate closed surface group acting properly discontuously on hyperbolic 3-space, {\Bbb H}^3, such that {\Bbb H}^3/\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.

2000 Subject Classification: 57M50.

Math. Annalen 332 (2005) 667-676.

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