Regularity of Kleinian limit sets and Patterson-Sullivan measures
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Date
01/10/2019Author
Grant ID
RF-2016-500
EP/R015104/1
Keywords
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Show full item recordAbstract
We consider several (related) notions of geometric regularity in the context of limit sets of geometrically finite Kleinian groups and associated Patterson-Sullivan measures. We begin by computing the upper and lower regularity dimensions of the Patterson-Sullivan measure, which involves controlling the relative measure of concentric balls. We then compute the Assouad and lower dimensions of the limit set, which involves controlling local doubling properties. Unlike the Hausdorff, packing, and box-counting dimensions, we show that the Assouad and lower dimensions are not necessarily given by the Poincaré exponent.
Citation
Fraser , J M 2019 , ' Regularity of Kleinian limit sets and Patterson-Sullivan measures ' , Transactions of the American Mathematical Society , vol. 372 , no. 7 , pp. 4977-5009 . https://doi.org/10.1090/tran/7830
Publication
Transactions of the American Mathematical Society
Status
Peer reviewed
ISSN
0002-9947Type
Journal article
Description
Funding: Leverhulme Trust Research Fellowship (RF-2016-500).Collections
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