On the isodiametric and isominwidth inequalities for planar bisections

For a given planar convex body K, a bisection of K is a decomposition of K into two closed sets A,B so that A∩B is an injective continuous curve connecting exactly two boundary points of K. Consider a bisection of K minimizing, over all bisections, the maximum diameter (resp., maximum width) of the...

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Detalles Bibliográficos
Autores: Cañete Martín, Antonio Jesús, González Merino, Bernardo
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2021
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/134619
Acceso en línea:https://hdl.handle.net/11441/134619
https://doi.org/10.4171/rmi/1225
Access Level:acceso abierto
Palabra clave:Planar convex bodies
Maximum bisecting diameter
Maximum bisecting width
Minimizing bisections
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spelling On the isodiametric and isominwidth inequalities for planar bisectionsCañete Martín, Antonio JesúsGonzález Merino, BernardoPlanar convex bodiesMaximum bisecting diameterMaximum bisecting widthMinimizing bisectionsFor a given planar convex body K, a bisection of K is a decomposition of K into two closed sets A,B so that A∩B is an injective continuous curve connecting exactly two boundary points of K. Consider a bisection of K minimizing, over all bisections, the maximum diameter (resp., maximum width) of the sets in the decomposition. In this note, we study some properties of these minimizing bisections and prove inequalities extending the classical isodiametric and isominwidth inequalities. Furthermore, we address the corresponding reverse optimization problems and establish inequalities similar to the reverse isodiametric and reverse isominwidth inequalities.Ministerio de Ciencia, Innovación y Universidades MTM2017-84851-C2-1-PJunta de Andalucía FQM-325Fundación Séneca 19901/GERM/15Ministerio de Ciencia, Innovación y Universidades PGC2018-094215-B-I00European Mathematical Society (EMS)Matemática Aplicada IMinisterio de Ciencia, Innovación y Universidades (MICINN). EspañaJunta de AndalucíaFundación Séneca2021info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/134619https://doi.org/10.4171/rmi/1225reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésRevista Matemática Iberoamericana, 37 (4), 1247-1275.MTM2017-84851-C2-1-PFQM-32519901/GERM/15PGC2018-094215-B-I00https://www.ems-ph.org/journals/show_abstract.php?issn=0213-2230&vol=37&iss=4&rank=2info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1346192026-06-17T12:51:07Z
dc.title.none.fl_str_mv On the isodiametric and isominwidth inequalities for planar bisections
title On the isodiametric and isominwidth inequalities for planar bisections
spellingShingle On the isodiametric and isominwidth inequalities for planar bisections
Cañete Martín, Antonio Jesús
Planar convex bodies
Maximum bisecting diameter
Maximum bisecting width
Minimizing bisections
title_short On the isodiametric and isominwidth inequalities for planar bisections
title_full On the isodiametric and isominwidth inequalities for planar bisections
title_fullStr On the isodiametric and isominwidth inequalities for planar bisections
title_full_unstemmed On the isodiametric and isominwidth inequalities for planar bisections
title_sort On the isodiametric and isominwidth inequalities for planar bisections
dc.creator.none.fl_str_mv Cañete Martín, Antonio Jesús
González Merino, Bernardo
author Cañete Martín, Antonio Jesús
author_facet Cañete Martín, Antonio Jesús
González Merino, Bernardo
author_role author
author2 González Merino, Bernardo
author2_role author
dc.contributor.none.fl_str_mv Matemática Aplicada I
Ministerio de Ciencia, Innovación y Universidades (MICINN). España
Junta de Andalucía
Fundación Séneca
dc.subject.none.fl_str_mv Planar convex bodies
Maximum bisecting diameter
Maximum bisecting width
Minimizing bisections
topic Planar convex bodies
Maximum bisecting diameter
Maximum bisecting width
Minimizing bisections
description For a given planar convex body K, a bisection of K is a decomposition of K into two closed sets A,B so that A∩B is an injective continuous curve connecting exactly two boundary points of K. Consider a bisection of K minimizing, over all bisections, the maximum diameter (resp., maximum width) of the sets in the decomposition. In this note, we study some properties of these minimizing bisections and prove inequalities extending the classical isodiametric and isominwidth inequalities. Furthermore, we address the corresponding reverse optimization problems and establish inequalities similar to the reverse isodiametric and reverse isominwidth inequalities.
publishDate 2021
dc.date.none.fl_str_mv 2021
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/134619
https://doi.org/10.4171/rmi/1225
url https://hdl.handle.net/11441/134619
https://doi.org/10.4171/rmi/1225
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Revista Matemática Iberoamericana, 37 (4), 1247-1275.
MTM2017-84851-C2-1-P
FQM-325
19901/GERM/15
PGC2018-094215-B-I00
https://www.ems-ph.org/journals/show_abstract.php?issn=0213-2230&vol=37&iss=4&rank=2
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv European Mathematical Society (EMS)
publisher.none.fl_str_mv European Mathematical Society (EMS)
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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