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dc.contributor.authorFraser, Jonathan MacDonald
dc.date.accessioned2019-06-07T23:39:29Z
dc.date.available2019-06-07T23:39:29Z
dc.date.issued2018-06-08
dc.identifier.citationFraser , J M 2018 , ' Distance sets, orthogonal projections, and passing to weak tangents ' , Israel Journal of Mathematics , vol. First Online . https://doi.org/10.1007/s11856-018-1715-zen
dc.identifier.issn0021-2172
dc.identifier.otherPURE: 250641852
dc.identifier.otherPURE UUID: bbf64538-b905-4e6d-bf74-e82197d955a5
dc.identifier.otherScopus: 85048250782
dc.identifier.otherORCID: /0000-0002-8066-9120/work/58285456
dc.identifier.otherWOS: 000437012800012
dc.identifier.urihttp://hdl.handle.net/10023/17849
dc.descriptionThe author is supported by a Leverhulme Trust Research Fellowship (RF-2016-500).en
dc.description.abstractWe consider the Assouad dimension analogues of two important problems in geometric measure theory. These problems are tied together by the common theme of ‘passing to weak tangents’. First, we solve the analogue of Falconer’s distance set problem for Assouad dimension in the plane: if a planar set has Assouad dimension greater than 1, then its distance set has Assouad dimension 1. We also obtain partial results in higher dimensions. Second, we consider how Assouad dimension behaves under orthogonal projection. We extend the planar projection theorem of Fraser and Orponen to higher dimensions, provide estimates on the (Hausdorff) dimension of the exceptional set of projections, and provide a recipe for obtaining results about restricted families of projections. We provide several illustrative examples throughout.
dc.format.extent25
dc.language.isoeng
dc.relation.ispartofIsrael Journal of Mathematicsen
dc.rights© 2018, Hebrew University of Jerusalem. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1007/s11856-018-1715-zen
dc.subjectAssouad dimensionen
dc.subjectWeak tangenten
dc.subjectDistance seten
dc.subjectOrthogonal projectionen
dc.subjectExceptional seten
dc.subjectRestricted familiesen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleDistance sets, orthogonal projections, and passing to weak tangentsen
dc.typeJournal articleen
dc.description.versionPostprinten
dc.contributor.institutionUniversity of St Andrews.Pure Mathematicsen
dc.identifier.doihttps://doi.org/10.1007/s11856-018-1715-z
dc.description.statusPeer revieweden
dc.date.embargoedUntil2019-06-08


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