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dc.contributor.authorFraser, Jonathan
dc.date.accessioned2022-12-09T12:30:02Z
dc.date.available2022-12-09T12:30:02Z
dc.date.issued2023-02-01
dc.identifier.citationFraser , J 2023 , ' A nonlinear projection theorem for Assouad dimension and applications ' , Journal of the London Mathematical Society , vol. 107 , no. 2 , pp. 777-797 . https://doi.org/10.1112/jlms.12697en
dc.identifier.issn0024-6107
dc.identifier.otherPURE: 281405648
dc.identifier.otherPURE UUID: 20f6b391-469a-47b0-b90e-0f6517d7c7d6
dc.identifier.otherORCID: /0000-0002-8066-9120/work/124490047
dc.identifier.otherScopus: 85144038187
dc.identifier.otherWOS: 000894167900001
dc.identifier.urihttps://hdl.handle.net/10023/26565
dc.descriptionFunding: The author was supported by an EPSRC Standard Grant (EP/R015104/1) and a Leverhulme Trust Research Project Grant (RPG-2019-034).en
dc.description.abstractWe prove a general nonlinear projection theorem for Assouad dimension. This theorem has several applications including to distance sets, radial projections, and sum-product phenomena. In the setting of distance sets we are able to completely resolve the planar version of Falconer’s distance set problem for Assouad dimension, both dealing with the awkward ‘critical case’ and providing sharp estimates for sets with Assouad dimension less than 1. In the higher dimensional setting we connect the problem to the dimension of the set of exceptions in a related (orthogonal) projection theorem. We also obtain results on pinned distance sets and our results still hold when distances are taken with respect to a sufficiently curved norm. As another application we prove a radial projection theorem for Assouad dimension with sharp estimates on the Hausdorff dimension of the exceptional set.
dc.format.extent21
dc.language.isoeng
dc.relation.ispartofJournal of the London Mathematical Societyen
dc.rightsCopyright © 2022 The Authors. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.en
dc.subjectAssouad dimensionen
dc.subjectNonlinear projectionsen
dc.subjectDistance setsen
dc.subjectRadial projectionsen
dc.subjectExceptional seten
dc.subjectHausdorff dimensionen
dc.subjectSum-product theoremen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subjectMCCen
dc.subject.lccQAen
dc.titleA nonlinear projection theorem for Assouad dimension and applicationsen
dc.typeJournal articleen
dc.contributor.sponsorEPSRCen
dc.contributor.sponsorThe Leverhulme Trusten
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.identifier.doihttps://doi.org/10.1112/jlms.12697
dc.description.statusPeer revieweden
dc.identifier.grantnumberEP/R015104/1en
dc.identifier.grantnumberRPG-2019-034en


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