The Minimal Volume of Simplices Containing a Convex Body

Autores
Galicer, Daniel Eric; Merzbacher, Diego Mariano; Pinasco, Damian
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let K⊂ Rn be a convex body with barycenter at the origin. We show there is a simplex S⊂ K having also barycenter at the origin such that (vol(S)vol(K))1/n≥cn, where c> 0 is an absolute constant. This is achieved using stochastic geometric techniques. Precisely, if K is in isotropic position, we present a method to find centered simplices verifying the above bound that works with extremely high probability. By duality, given a convex body K⊂ Rn we show there is a simplex S enclosing Kwith the same barycenter such that(vol(S)vol(K))1/n≤dn,for some absolute constant d> 0. Up to the constant, the estimate cannot be lessened.
Fil: Galicer, Daniel Eric. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Merzbacher, Diego Mariano. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Pinasco, Damian. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
CONVEX BODIES
ISOTROPIC POSITION
RANDOM SIMPLICES
SIMPLICES
VOLUME RATIO
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:11336/116939
Acceder
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network_name_str CONICET Digital (CONICET)
spelling The Minimal Volume of Simplices Containing a Convex BodyGalicer, Daniel EricMerzbacher, Diego MarianoPinasco, DamianCONVEX BODIESISOTROPIC POSITIONRANDOM SIMPLICESSIMPLICESVOLUME RATIOhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let K⊂ Rn be a convex body with barycenter at the origin. We show there is a simplex S⊂ K having also barycenter at the origin such that (vol(S)vol(K))1/n≥cn, where c> 0 is an absolute constant. This is achieved using stochastic geometric techniques. Precisely, if K is in isotropic position, we present a method to find centered simplices verifying the above bound that works with extremely high probability. By duality, given a convex body K⊂ Rn we show there is a simplex S enclosing Kwith the same barycenter such that(vol(S)vol(K))1/n≤dn,for some absolute constant d> 0. Up to the constant, the estimate cannot be lessened.Fil: Galicer, Daniel Eric. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Merzbacher, Diego Mariano. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Pinasco, Damian. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaSpringer2019-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/116939Galicer, Daniel Eric; Merzbacher, Diego Mariano; Pinasco, Damian; The Minimal Volume of Simplices Containing a Convex Body; Springer; The Journal Of Geometric Analysis; 29; 1; 1-2019; 717-7321050-6926CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs12220-018-0016-4info:eu-repo/semantics/altIdentifier/doi/10.1007/s12220-018-0016-4info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:02:07Zoai:ri.conicet.gov.ar:11336/116939instacron: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:34982025-09-03 10:02:07.853CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The Minimal Volume of Simplices Containing a Convex Body
title The Minimal Volume of Simplices Containing a Convex Body
spellingShingle The Minimal Volume of Simplices Containing a Convex Body
Galicer, Daniel Eric
CONVEX BODIES
ISOTROPIC POSITION
RANDOM SIMPLICES
SIMPLICES
VOLUME RATIO
title_short The Minimal Volume of Simplices Containing a Convex Body
title_full The Minimal Volume of Simplices Containing a Convex Body
title_fullStr The Minimal Volume of Simplices Containing a Convex Body
title_full_unstemmed The Minimal Volume of Simplices Containing a Convex Body
title_sort The Minimal Volume of Simplices Containing a Convex Body
dc.creator.none.fl_str_mv Galicer, Daniel Eric
Merzbacher, Diego Mariano
Pinasco, Damian
author Galicer, Daniel Eric
author_facet Galicer, Daniel Eric
Merzbacher, Diego Mariano
Pinasco, Damian
author_role author
author2 Merzbacher, Diego Mariano
Pinasco, Damian
author2_role author
author
dc.subject.none.fl_str_mv CONVEX BODIES
ISOTROPIC POSITION
RANDOM SIMPLICES
SIMPLICES
VOLUME RATIO
topic CONVEX BODIES
ISOTROPIC POSITION
RANDOM SIMPLICES
SIMPLICES
VOLUME RATIO
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let K⊂ Rn be a convex body with barycenter at the origin. We show there is a simplex S⊂ K having also barycenter at the origin such that (vol(S)vol(K))1/n≥cn, where c> 0 is an absolute constant. This is achieved using stochastic geometric techniques. Precisely, if K is in isotropic position, we present a method to find centered simplices verifying the above bound that works with extremely high probability. By duality, given a convex body K⊂ Rn we show there is a simplex S enclosing Kwith the same barycenter such that(vol(S)vol(K))1/n≤dn,for some absolute constant d> 0. Up to the constant, the estimate cannot be lessened.
Fil: Galicer, Daniel Eric. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Merzbacher, Diego Mariano. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Pinasco, Damian. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description Let K⊂ Rn be a convex body with barycenter at the origin. We show there is a simplex S⊂ K having also barycenter at the origin such that (vol(S)vol(K))1/n≥cn, where c> 0 is an absolute constant. This is achieved using stochastic geometric techniques. Precisely, if K is in isotropic position, we present a method to find centered simplices verifying the above bound that works with extremely high probability. By duality, given a convex body K⊂ Rn we show there is a simplex S enclosing Kwith the same barycenter such that(vol(S)vol(K))1/n≤dn,for some absolute constant d> 0. Up to the constant, the estimate cannot be lessened.
publishDate 2019
dc.date.none.fl_str_mv 2019-01
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/11336/116939
Galicer, Daniel Eric; Merzbacher, Diego Mariano; Pinasco, Damian; The Minimal Volume of Simplices Containing a Convex Body; Springer; The Journal Of Geometric Analysis; 29; 1; 1-2019; 717-732
1050-6926
CONICET Digital
CONICET
url http://hdl.handle.net/11336/116939
identifier_str_mv Galicer, Daniel Eric; Merzbacher, Diego Mariano; Pinasco, Damian; The Minimal Volume of Simplices Containing a Convex Body; Springer; The Journal Of Geometric Analysis; 29; 1; 1-2019; 717-732
1050-6926
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://link.springer.com/article/10.1007%2Fs12220-018-0016-4
info:eu-repo/semantics/altIdentifier/doi/10.1007/s12220-018-0016-4
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/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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 13.13397

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