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Assouad dimension influences the box and packing dimensions of orthogonal projections

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dc.contributor.authorFalconer, Kenneth John
dc.contributor.authorFraser, Jonathan
dc.contributor.authorShmerkin, Pablo
dc.date.accessioned2020-03-13T10:30:01Z
dc.date.available2020-03-13T10:30:01Z
dc.date.issued2021
dc.identifier266855607
dc.identifierf689197c-7dc2-4753-a253-f40d412e11b3
dc.identifier85116598954
dc.identifier000698564300002
dc.identifier.citationFalconer , K J , Fraser , J & Shmerkin , P 2021 , ' Assouad dimension influences the box and packing dimensions of orthogonal projections ' , Journal of Fractal Geometry , vol. 8 , no. 3 , pp. 247–259 . https://doi.org/10.4171/jfg/104en
dc.identifier.issn2308-1309
dc.identifier.otherORCID: /0000-0001-8823-0406/work/93894039
dc.identifier.otherORCID: /0000-0002-8066-9120/work/93894217
dc.identifier.urihttps://hdl.handle.net/10023/19646
dc.descriptionFunding: UK EPSRC Standard Grant (EP/R015104/1) (KJF and JMF). Leverhulme Trust Research Project Grant (RPG-2019-034) (JMF). Royal Society International Exchange grant IES\R1\191195 (KJF and PS). ProjectPICT 2015-3675 (ANPCyT) (PS).en
dc.description.abstractWe present several applications of the Assouad dimension, and the related quasi-Assouad dimension and Assouad spectrum, to the box and packing dimensions of orthogonal projections of sets. For example, we show that if the (quasi-)Assouad dimension of F ⊆ R n is no greater than m, then the box and packing dimensions of F are preserved under orthogonal projections onto almost all m-dimensional subspaces. We also show that the threshold m for the (quasi-)Assouad dimension is sharp, and bound the dimension of the exceptional set of projections strictly away from the dimension of the Grassmannian.
dc.format.extent169223
dc.language.isoeng
dc.relation.ispartofJournal of Fractal Geometryen
dc.rightsCopyright © 2021 European Mathematical Society Published by EMS Press This work is licensed under a CC BY 4.0 license.en
dc.subjectAssouad dimensionen
dc.subjectBox dimensionen
dc.subjectPacking dimensionen
dc.subjectOrthogonal projectionen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleAssouad dimension influences the box and packing dimensions of orthogonal projectionsen
dc.typeJournal articleen
dc.contributor.sponsorEPSRCen
dc.contributor.sponsorThe Leverhulme Trusten
dc.contributor.institutionUniversity of St Andrews.Pure Mathematicsen
dc.identifier.doi10.4171/jfg/104
dc.description.statusPeer revieweden
dc.identifier.urlhttps://arxiv.org/abs/1911.04857en
dc.identifier.urlhttps://ems.press/journals/jfg/articles/985977en
dc.identifier.grantnumberEP/R015104/1en
dc.identifier.grantnumberRPG-2019-034en


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