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dc.contributor.authorFraser, Jonathan MacDonald
dc.contributor.authorOlson, Eric
dc.contributor.authorRobinson, James
dc.date.accessioned2019-03-01T09:30:21Z
dc.date.available2019-03-01T09:30:21Z
dc.date.issued2017-10-01
dc.identifier.citationFraser , J M , Olson , E & Robinson , J 2017 , ' Some results in support of the Kakeya conjecture ' , Real Analysis Exchange , vol. 42 , no. 2 , pp. 253-268 . https://doi.org/10.14321/realanalexch.42.2.0253en
dc.identifier.issn0147-1937
dc.identifier.otherPURE: 249921410
dc.identifier.otherPURE UUID: 4eacb186-44fa-4142-a5b1-a6cb6addec4f
dc.identifier.otherScopus: 85041600211
dc.identifier.otherORCID: /0000-0002-8066-9120/work/58285479
dc.identifier.otherWOS: 000431996500002
dc.identifier.urihttps://hdl.handle.net/10023/17184
dc.descriptionJMF was supported by the EPSRC grant EP/J013560/1 when at the University of Warwick and by the Leverhulme Trust Research Fellowship RF-2016-500 when at the University of St Andrews (current).en
dc.description.abstractA Besicovitch set is a subset of Rd that contains a unit line segment in every direction and the famous Kakeya conjecture states that Besicovitch sets should have full dimension. We provide a number of results in support of this conjecture in a variety of contexts. Our proofs are simple and aim to give an intuitive feel for the problem. For example, we give a very simple proof that the packing and lower box-counting dimension of any Besicovitch set is at least (d+1)/2 (better estimates are available in the literature). We also study the 'generic validity' of the Kakeya conjecture in the setting of Baire Category and prove that typical Besicovitch sets have full upper box-counting dimension. We also study a weaker version of the Kakeya problem where unit line segments are replaced by half-infinite lines. We prove that such 'half-extended Besicovitch sets' have full Assouad dimension. This can be viewed as full resolution of a (much weakened) version of the Kakeya problem.
dc.language.isoeng
dc.relation.ispartofReal Analysis Exchangeen
dc.rights© 2017, Real Analysis Exchange. 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/10.14321/realanalexch.42.2.0253en
dc.subjectKakeya conjectureen
dc.subjectbox counting dimensionen
dc.subjectHausdorff dimensionen
dc.subjectAssouad dimensionen
dc.subjectBaire categoryen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleSome results in support of the Kakeya conjectureen
dc.typeJournal articleen
dc.contributor.sponsorThe Leverhulme Trusten
dc.description.versionPostprinten
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.identifier.doihttps://doi.org/10.14321/realanalexch.42.2.0253
dc.description.statusPeer revieweden
dc.date.embargoedUntil2018-10-01
dc.identifier.urlhttps://arxiv.org/abs/1407.6689en
dc.identifier.grantnumberRF-2016-500en


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