Hölder coverings of sets of small dimension

Autores
Rossi, Eino Vihtori; Shmerkin, Pablo Sebastian
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We show that a set of small box counting dimension can be covered by a H¨older graph from all but a small set of directions, and give sharp bounds for the dimension of the exceptional set, improving a result of B. Hunt and V. Kaloshin. We observe that, as a consequence, H¨older graphs can have positive doubling measure, answering a question of T. Ojala and T. Rajala. We also give remarks on H¨older coverings in polar coordinates and, on the other hand, prove that a Homogenous set of small box counting dimension can be covered by a Lipschitz graph from all but a small set of directions.
Fil: Rossi, Eino Vihtori. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Shmerkin, Pablo Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina
Materia
BOX DIMENSION
HOLDER GRAPH
THIN SETS
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:11336/131239
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/131239
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Hölder coverings of sets of small dimensionRossi, Eino VihtoriShmerkin, Pablo SebastianBOX DIMENSIONHOLDER GRAPHTHIN SETShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We show that a set of small box counting dimension can be covered by a H¨older graph from all but a small set of directions, and give sharp bounds for the dimension of the exceptional set, improving a result of B. Hunt and V. Kaloshin. We observe that, as a consequence, H¨older graphs can have positive doubling measure, answering a question of T. Ojala and T. Rajala. We also give remarks on H¨older coverings in polar coordinates and, on the other hand, prove that a Homogenous set of small box counting dimension can be covered by a Lipschitz graph from all but a small set of directions.Fil: Rossi, Eino Vihtori. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Shmerkin, Pablo Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; ArgentinaEuropean Mathematical Society2019-06-24info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/pdfhttp://hdl.handle.net/11336/131239Rossi, Eino Vihtori; Shmerkin, Pablo Sebastian; Hölder coverings of sets of small dimension; European Mathematical Society; Journal of Fractal Geometry; 6; 3; 24-6-2019; 285-2992308-13092308-1317CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.4171/JFG/78info:eu-repo/semantics/altIdentifier/url/https://www.ems-ph.org/journals/show_abstract.php?issn=2308-1309&vol=6&iss=3&rank=4info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-12T09:50:43Zoai:ri.conicet.gov.ar:11336/131239instacron: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:34982025-11-12 09:50:43.326CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Hölder coverings of sets of small dimension
title Hölder coverings of sets of small dimension
spellingShingle Hölder coverings of sets of small dimension
Rossi, Eino Vihtori
BOX DIMENSION
HOLDER GRAPH
THIN SETS
title_short Hölder coverings of sets of small dimension
title_full Hölder coverings of sets of small dimension
title_fullStr Hölder coverings of sets of small dimension
title_full_unstemmed Hölder coverings of sets of small dimension
title_sort Hölder coverings of sets of small dimension
dc.creator.none.fl_str_mv Rossi, Eino Vihtori
Shmerkin, Pablo Sebastian
author Rossi, Eino Vihtori
author_facet Rossi, Eino Vihtori
Shmerkin, Pablo Sebastian
author_role author
author2 Shmerkin, Pablo Sebastian
author2_role author
dc.subject.none.fl_str_mv BOX DIMENSION
HOLDER GRAPH
THIN SETS
topic BOX DIMENSION
HOLDER GRAPH
THIN SETS
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 show that a set of small box counting dimension can be covered by a H¨older graph from all but a small set of directions, and give sharp bounds for the dimension of the exceptional set, improving a result of B. Hunt and V. Kaloshin. We observe that, as a consequence, H¨older graphs can have positive doubling measure, answering a question of T. Ojala and T. Rajala. We also give remarks on H¨older coverings in polar coordinates and, on the other hand, prove that a Homogenous set of small box counting dimension can be covered by a Lipschitz graph from all but a small set of directions.
Fil: Rossi, Eino Vihtori. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Shmerkin, Pablo Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina
description We show that a set of small box counting dimension can be covered by a H¨older graph from all but a small set of directions, and give sharp bounds for the dimension of the exceptional set, improving a result of B. Hunt and V. Kaloshin. We observe that, as a consequence, H¨older graphs can have positive doubling measure, answering a question of T. Ojala and T. Rajala. We also give remarks on H¨older coverings in polar coordinates and, on the other hand, prove that a Homogenous set of small box counting dimension can be covered by a Lipschitz graph from all but a small set of directions.
publishDate 2019
dc.date.none.fl_str_mv 2019-06-24
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/11336/131239
Rossi, Eino Vihtori; Shmerkin, Pablo Sebastian; Hölder coverings of sets of small dimension; European Mathematical Society; Journal of Fractal Geometry; 6; 3; 24-6-2019; 285-299
2308-1309
2308-1317
CONICET Digital
CONICET
url http://hdl.handle.net/11336/131239
identifier_str_mv Rossi, Eino Vihtori; Shmerkin, Pablo Sebastian; Hölder coverings of sets of small dimension; European Mathematical Society; Journal of Fractal Geometry; 6; 3; 24-6-2019; 285-299
2308-1309
2308-1317
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.4171/JFG/78
info:eu-repo/semantics/altIdentifier/url/https://www.ems-ph.org/journals/show_abstract.php?issn=2308-1309&vol=6&iss=3&rank=4
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/zip
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
_version_ 1848598119300726784
score 12.976206

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