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Regularity of Kleinian limit sets and Patterson-Sullivan measures
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dc.contributor.author | Fraser, Jonathan MacDonald | |
dc.date.accessioned | 2019-02-20T13:30:04Z | |
dc.date.available | 2019-02-20T13:30:04Z | |
dc.date.issued | 2019-10-01 | |
dc.identifier | 257794598 | |
dc.identifier | 77640b52-c55f-431f-8512-3a870fd468b8 | |
dc.identifier | 85075117957 | |
dc.identifier | 000487086300016 | |
dc.identifier.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 | en |
dc.identifier.issn | 0002-9947 | |
dc.identifier.other | ORCID: /0000-0002-8066-9120/work/58984318 | |
dc.identifier.uri | https://hdl.handle.net/10023/17101 | |
dc.description | Funding: Leverhulme Trust Research Fellowship (RF-2016-500). | en |
dc.description.abstract | 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. | |
dc.format.extent | 33 | |
dc.format.extent | 499242 | |
dc.language.iso | eng | |
dc.relation.ispartof | Transactions of the American Mathematical Society | en |
dc.subject | Kleinian group | en |
dc.subject | Patterson-Sullivan measure | en |
dc.subject | Assouad dimension | en |
dc.subject | Regularity dimension | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject | BDC | en |
dc.subject | R2C | en |
dc.subject.lcc | QA | en |
dc.title | Regularity of Kleinian limit sets and Patterson-Sullivan measures | en |
dc.type | Journal article | en |
dc.contributor.sponsor | The Leverhulme Trust | en |
dc.contributor.sponsor | EPSRC | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | 10.1090/tran/7830 | |
dc.description.status | Peer reviewed | en |
dc.identifier.grantnumber | RF-2016-500 | en |
dc.identifier.grantnumber | EP/R015104/1 | en |
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