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dc.contributor.authorFraser, Jonathan MacDonald
dc.date.accessioned2019-02-20T13:30:04Z
dc.date.available2019-02-20T13:30:04Z
dc.date.issued2019-10-01
dc.identifier257794598
dc.identifier77640b52-c55f-431f-8512-3a870fd468b8
dc.identifier85075117957
dc.identifier000487086300016
dc.identifier.citationFraser , 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/7830en
dc.identifier.issn0002-9947
dc.identifier.otherORCID: /0000-0002-8066-9120/work/58984318
dc.identifier.urihttps://hdl.handle.net/10023/17101
dc.descriptionFunding: Leverhulme Trust Research Fellowship (RF-2016-500).en
dc.description.abstractWe 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.extent33
dc.format.extent499242
dc.language.isoeng
dc.relation.ispartofTransactions of the American Mathematical Societyen
dc.subjectKleinian groupen
dc.subjectPatterson-Sullivan measureen
dc.subjectAssouad dimensionen
dc.subjectRegularity dimensionen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subjectBDCen
dc.subjectR2Cen
dc.subject.lccQAen
dc.titleRegularity of Kleinian limit sets and Patterson-Sullivan measuresen
dc.typeJournal articleen
dc.contributor.sponsorThe Leverhulme Trusten
dc.contributor.sponsorEPSRCen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.identifier.doi10.1090/tran/7830
dc.description.statusPeer revieweden
dc.identifier.grantnumberRF-2016-500en
dc.identifier.grantnumberEP/R015104/1en


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