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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.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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