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arXiv · 1408.4664

On interpreting Patterson--Sullivan measures of geometrically finite groups as Hausdorff and packing measures

David Simmons
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Abstract

We provide a new proof of a theorem whose proof was sketched by Sullivan ('82), namely that if the Poincar\'e exponent of a geometrically finite Kleinian group $G$ is strictly between its minimal and maximal cusp ranks, then the Patterson--Sullivan measure of $G$ is not proportional to the Hausdorff or packing measure of any gauge function. This disproves a conjecture of Stratmann ('97, '06).

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David Simmons. 2014-08-20. On interpreting Patterson--Sullivan measures of geometrically finite groups as Hausdorff and packing measures. https://arxiv.org/abs/1408.4664

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