Assouad dimension influences the box and packing dimensions of orthogonal projections

Autores
Falconer, Kenneth J.; Fraser, Jonathan M.; Shmerkin, Pablo Sebastian
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
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.
Fil: Falconer, Kenneth J.. University of St. Andrews; Reino Unido
Fil: Fraser, Jonathan M.. University of St. Andrews; Reino Unido
Fil: Shmerkin, Pablo Sebastian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
ASSOUAD DIMENSION
BOX DIMENSION
PACKING DIMENSION
ORTHOGONAL PROJECTIONS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/155243
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/155243
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Assouad dimension influences the box and packing dimensions of orthogonal projectionsFalconer, Kenneth J.Fraser, Jonathan M.Shmerkin, Pablo SebastianASSOUAD DIMENSIONBOX DIMENSIONPACKING DIMENSIONORTHOGONAL PROJECTIONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We 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.Fil: Falconer, Kenneth J.. University of St. Andrews; Reino UnidoFil: Fraser, Jonathan M.. University of St. Andrews; Reino UnidoFil: Shmerkin, Pablo Sebastian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaEuropean Mathematical Society2021-05-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/155243Falconer, 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; 247–2592308-1309CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.ems-ph.org/doi/10.4171/JFG/104info:eu-repo/semantics/altIdentifier/doi/10.4171/JFG/104info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1911.04857info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:40:59Zoai:ri.conicet.gov.ar:11336/155243instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:40:59.593CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Assouad dimension influences the box and packing dimensions of orthogonal projections
title Assouad dimension influences the box and packing dimensions of orthogonal projections
spellingShingle Assouad dimension influences the box and packing dimensions of orthogonal projections
Falconer, Kenneth J.
ASSOUAD DIMENSION
BOX DIMENSION
PACKING DIMENSION
ORTHOGONAL PROJECTIONS
title_short Assouad dimension influences the box and packing dimensions of orthogonal projections
title_full Assouad dimension influences the box and packing dimensions of orthogonal projections
title_fullStr Assouad dimension influences the box and packing dimensions of orthogonal projections
title_full_unstemmed Assouad dimension influences the box and packing dimensions of orthogonal projections
title_sort Assouad dimension influences the box and packing dimensions of orthogonal projections
dc.creator.none.fl_str_mv Falconer, Kenneth J.
Fraser, Jonathan M.
Shmerkin, Pablo Sebastian
author Falconer, Kenneth J.
author_facet Falconer, Kenneth J.
Fraser, Jonathan M.
Shmerkin, Pablo Sebastian
author_role author
author2 Fraser, Jonathan M.
Shmerkin, Pablo Sebastian
author2_role author
author
dc.subject.none.fl_str_mv ASSOUAD DIMENSION
BOX DIMENSION
PACKING DIMENSION
ORTHOGONAL PROJECTIONS
topic ASSOUAD DIMENSION
BOX DIMENSION
PACKING DIMENSION
ORTHOGONAL PROJECTIONS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv 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.
Fil: Falconer, Kenneth J.. University of St. Andrews; Reino Unido
Fil: Fraser, Jonathan M.. University of St. Andrews; Reino Unido
Fil: Shmerkin, Pablo Sebastian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description 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.
publishDate 2021
dc.date.none.fl_str_mv 2021-05-03
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/155243
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
2308-1309
CONICET Digital
CONICET
url http://hdl.handle.net/11336/155243
identifier_str_mv 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
2308-1309
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.ems-ph.org/doi/10.4171/JFG/104
info:eu-repo/semantics/altIdentifier/doi/10.4171/JFG/104
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1911.04857
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv European Mathematical Society
publisher.none.fl_str_mv European Mathematical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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