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

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JournalErgodic Theory and Dynamical Systems
DateAccepted/In press - 2015
DateE-pub ahead of print - 21 Jul 2015
DatePublished (current) - 1 Dec 2016
Issue number8
Number of pages12
Pages (from-to)2675-2686
Early online date21/07/15
Original languageEnglish


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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  • math.DS

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