The Santaló point for the Holmes-Thompson boundary area

We explore the notion of Santaló point for the Holmes-Thompson boundary area of a convex body in a normed space. In the case where the norm is C, and in the case where unit ball and convex body coincide, we prove existence and uniqueness. When the normed space has a smooth positively curved unit bal...

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Autores: Balacheff, Florent Nicolas|||0000-0001-9770-2954, Solanes, Gil|||0000-0001-5518-5530, Tzanev, Kroum
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:250618
Acceso en línea:https://ddd.uab.cat/record/250618
https://dx.doi.org/urn:doi:10.1016/j.aim.2021.108118
Access Level:acceso abierto
Palabra clave:Convex body
Crofton formula
Holmes-Thompson area and volume
Minkowski geometry
Santaló point
Symplectic geometry
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spelling The Santaló point for the Holmes-Thompson boundary areaBalacheff, Florent Nicolas|||0000-0001-9770-2954Solanes, Gil|||0000-0001-5518-5530Tzanev, KroumConvex bodyCrofton formulaHolmes-Thompson area and volumeMinkowski geometrySantaló pointSymplectic geometryWe explore the notion of Santaló point for the Holmes-Thompson boundary area of a convex body in a normed space. In the case where the norm is C, and in the case where unit ball and convex body coincide, we prove existence and uniqueness. When the normed space has a smooth positively curved unit ball, we exhibit a dual Santaló point expressed as an average of centroids of projections of the dual body. 22021-01-0120212021-01-01Articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/250618https://dx.doi.org/urn:doi:10.1016/j.aim.2021.108118reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Economía, Industria y Competitividad https://doi.org/10.13039/501100010198 RYC-2016-19334Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 PGC2018-095998-B-I00Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1725open accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2506182026-06-06T12:50:31Z
dc.title.none.fl_str_mv The Santaló point for the Holmes-Thompson boundary area
title The Santaló point for the Holmes-Thompson boundary area
spellingShingle The Santaló point for the Holmes-Thompson boundary area
Balacheff, Florent Nicolas|||0000-0001-9770-2954
Convex body
Crofton formula
Holmes-Thompson area and volume
Minkowski geometry
Santaló point
Symplectic geometry
title_short The Santaló point for the Holmes-Thompson boundary area
title_full The Santaló point for the Holmes-Thompson boundary area
title_fullStr The Santaló point for the Holmes-Thompson boundary area
title_full_unstemmed The Santaló point for the Holmes-Thompson boundary area
title_sort The Santaló point for the Holmes-Thompson boundary area
dc.creator.none.fl_str_mv Balacheff, Florent Nicolas|||0000-0001-9770-2954
Solanes, Gil|||0000-0001-5518-5530
Tzanev, Kroum
author Balacheff, Florent Nicolas|||0000-0001-9770-2954
author_facet Balacheff, Florent Nicolas|||0000-0001-9770-2954
Solanes, Gil|||0000-0001-5518-5530
Tzanev, Kroum
author_role author
author2 Solanes, Gil|||0000-0001-5518-5530
Tzanev, Kroum
author2_role author
author
dc.subject.none.fl_str_mv Convex body
Crofton formula
Holmes-Thompson area and volume
Minkowski geometry
Santaló point
Symplectic geometry
topic Convex body
Crofton formula
Holmes-Thompson area and volume
Minkowski geometry
Santaló point
Symplectic geometry
description We explore the notion of Santaló point for the Holmes-Thompson boundary area of a convex body in a normed space. In the case where the norm is C, and in the case where unit ball and convex body coincide, we prove existence and uniqueness. When the normed space has a smooth positively curved unit ball, we exhibit a dual Santaló point expressed as an average of centroids of projections of the dual body.
publishDate 2021
dc.date.none.fl_str_mv 2
2021-01-01
2021
2021-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/250618
https://dx.doi.org/urn:doi:10.1016/j.aim.2021.108118
url https://ddd.uab.cat/record/250618
https://dx.doi.org/urn:doi:10.1016/j.aim.2021.108118
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía, Industria y Competitividad https://doi.org/10.13039/501100010198 RYC-2016-19334
Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 PGC2018-095998-B-I00
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1725
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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