On the Hausdorff dimension of pinned distance sets

Autores
Shmerkin, Pablo Sebastian
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We prove that if A is a Borel set in the plane of equal Hausdorff and packing dimension s > 1, then the set of pinned distances {|x − y| : y ∈ A} has full Hausdorff dimension for all x outside of a set of Hausdorff dimension 1 (in particular, for many x ∈ A). This verifies a strong variant of Falconer’s distance set conjecture for sets of equal Hausdorff and packing dimension, outside the endpoint s = 1.
Fil: Shmerkin, Pablo Sebastian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Distance sets
Hausdorff dimension
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/122819
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/122819
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling On the Hausdorff dimension of pinned distance setsShmerkin, Pablo SebastianDistance setsHausdorff dimensionhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We prove that if A is a Borel set in the plane of equal Hausdorff and packing dimension s > 1, then the set of pinned distances {|x − y| : y ∈ A} has full Hausdorff dimension for all x outside of a set of Hausdorff dimension 1 (in particular, for many x ∈ A). This verifies a strong variant of Falconer’s distance set conjecture for sets of equal Hausdorff and packing dimension, outside the endpoint s = 1.Fil: Shmerkin, Pablo Sebastian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaHebrew Univ Magnes Press2019-04-17info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/122819Shmerkin, Pablo Sebastian; On the Hausdorff dimension of pinned distance sets; Hebrew Univ Magnes Press; Israel Journal Of Mathematics; 230; 2; 17-4-2019; 949-9720021-2172CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/s11856-019-1847-9info:eu-repo/semantics/altIdentifier/doi/10.1007/s11856-019-1847-9info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T09:35:23Zoai:ri.conicet.gov.ar:11336/122819instacron: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:34982025-11-05 09:35:23.369CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the Hausdorff dimension of pinned distance sets
title On the Hausdorff dimension of pinned distance sets
spellingShingle On the Hausdorff dimension of pinned distance sets
Shmerkin, Pablo Sebastian
Distance sets
Hausdorff dimension
title_short On the Hausdorff dimension of pinned distance sets
title_full On the Hausdorff dimension of pinned distance sets
title_fullStr On the Hausdorff dimension of pinned distance sets
title_full_unstemmed On the Hausdorff dimension of pinned distance sets
title_sort On the Hausdorff dimension of pinned distance sets
dc.creator.none.fl_str_mv Shmerkin, Pablo Sebastian
author Shmerkin, Pablo Sebastian
author_facet Shmerkin, Pablo Sebastian
author_role author
dc.subject.none.fl_str_mv Distance sets
Hausdorff dimension
topic Distance sets
Hausdorff dimension
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 prove that if A is a Borel set in the plane of equal Hausdorff and packing dimension s > 1, then the set of pinned distances {|x − y| : y ∈ A} has full Hausdorff dimension for all x outside of a set of Hausdorff dimension 1 (in particular, for many x ∈ A). This verifies a strong variant of Falconer’s distance set conjecture for sets of equal Hausdorff and packing dimension, outside the endpoint s = 1.
Fil: Shmerkin, Pablo Sebastian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We prove that if A is a Borel set in the plane of equal Hausdorff and packing dimension s > 1, then the set of pinned distances {|x − y| : y ∈ A} has full Hausdorff dimension for all x outside of a set of Hausdorff dimension 1 (in particular, for many x ∈ A). This verifies a strong variant of Falconer’s distance set conjecture for sets of equal Hausdorff and packing dimension, outside the endpoint s = 1.
publishDate 2019
dc.date.none.fl_str_mv 2019-04-17
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/11336/122819
Shmerkin, Pablo Sebastian; On the Hausdorff dimension of pinned distance sets; Hebrew Univ Magnes Press; Israel Journal Of Mathematics; 230; 2; 17-4-2019; 949-972
0021-2172
CONICET Digital
CONICET
url http://hdl.handle.net/11336/122819
identifier_str_mv Shmerkin, Pablo Sebastian; On the Hausdorff dimension of pinned distance sets; Hebrew Univ Magnes Press; Israel Journal Of Mathematics; 230; 2; 17-4-2019; 949-972
0021-2172
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/s11856-019-1847-9
info:eu-repo/semantics/altIdentifier/doi/10.1007/s11856-019-1847-9
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Hebrew Univ Magnes Press
publisher.none.fl_str_mv Hebrew Univ Magnes Press
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 13.087074

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