, Volume 332, Issue 3, pp 667-676
Date: 07 May 2005

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, H 3, such that H 3/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.