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dc.contributor.author
Falconer, Kenneth J.
dc.contributor.author
Fraser, Jonathan M.
dc.contributor.author
Shmerkin, Pablo Sebastian
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dc.date.available
2022-04-13T18:40:23Z
dc.date.issued
2021-05-03
dc.identifier.citation
Falconer, Kenneth J.; Fraser, Jonathan M.; Shmerkin, Pablo Sebastian; Assouad dimension influences the box and packing dimensions of orthogonal projections; European Mathematical Society; Journal of Fractal Geometry; 8; 3; 3-5-2021; 247–259
dc.identifier.uri
http://hdl.handle.net/11336/155243
dc.description.abstract
We 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⊆Rn 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
application/pdf
dc.language.iso
eng
dc.publisher
European Mathematical Society
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.subject
ASSOUAD DIMENSION
dc.subject
BOX DIMENSION
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PACKING DIMENSION
dc.subject
ORTHOGONAL PROJECTIONS
dc.subject.classification
Matemática Pura
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dc.subject.classification
Matemáticas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.title
Assouad dimension influences the box and packing dimensions of orthogonal projections
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2022-04-07T21:05:20Z
dc.identifier.eissn
2308-1309
dc.journal.volume
8
dc.journal.number
3
dc.journal.pagination
247–259
dc.journal.pais
Suiza
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dc.description.fil
Fil: Falconer, Kenneth J.. University of St. Andrews; Reino Unido
dc.description.fil
Fil: Fraser, Jonathan M.. University of St. Andrews; Reino Unido
dc.description.fil
Fil: Shmerkin, Pablo Sebastian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
dc.journal.title
Journal of Fractal Geometry
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.ems-ph.org/doi/10.4171/JFG/104
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.4171/JFG/104
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1911.04857
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