A property of the planar measure of the lemniscates

Autores
Cuenya, Hector Hugo; Levis, Fabián Eduardo
Año de publicación
2007
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, we establish the following conjecture: There exists a constant K such that every lemniscate E(a,c), a Î C^n, c>0, contains a disk B(a, c) with mu(E(a, c)) £ Kmu(B(a, c)), where mu is the planar measure. We prove this conjecture for any family of lemniscates with at the most three foci and for any family of lemniscates where its foci satisfy a suitable condition.
Fil: Cuenya, Hector Hugo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; Argentina
Fil: Levis, Fabián Eduardo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
Materia
LEMNISCATES
PLANAR MEASURE
INEQUALITIES
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:11336/242026
Acceder
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network_name_str CONICET Digital (CONICET)
spelling A property of the planar measure of the lemniscatesCuenya, Hector HugoLevis, Fabián EduardoLEMNISCATESPLANAR MEASUREINEQUALITIEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper, we establish the following conjecture: There exists a constant K such that every lemniscate E(a,c), a Î C^n, c>0, contains a disk B(a, c) with mu(E(a, c)) £ Kmu(B(a, c)), where mu is the planar measure. We prove this conjecture for any family of lemniscates with at the most three foci and for any family of lemniscates where its foci satisfy a suitable condition.Fil: Cuenya, Hector Hugo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; ArgentinaFil: Levis, Fabián Eduardo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaAcademic Press Inc Elsevier Science2007-12info: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/11336/242026Cuenya, Hector Hugo; Levis, Fabián Eduardo; A property of the planar measure of the lemniscates; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 336; 2; 12-2007; 953-9610022-247XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022247X07003319info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2007.03.034info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2026-02-26T10:22:56Zoai:ri.conicet.gov.ar:11336/242026instacron: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:34982026-02-26 10:22:56.39CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A property of the planar measure of the lemniscates
title A property of the planar measure of the lemniscates
spellingShingle A property of the planar measure of the lemniscates
Cuenya, Hector Hugo
LEMNISCATES
PLANAR MEASURE
INEQUALITIES
title_short A property of the planar measure of the lemniscates
title_full A property of the planar measure of the lemniscates
title_fullStr A property of the planar measure of the lemniscates
title_full_unstemmed A property of the planar measure of the lemniscates
title_sort A property of the planar measure of the lemniscates
dc.creator.none.fl_str_mv Cuenya, Hector Hugo
Levis, Fabián Eduardo
author Cuenya, Hector Hugo
author_facet Cuenya, Hector Hugo
Levis, Fabián Eduardo
author_role author
author2 Levis, Fabián Eduardo
author2_role author
dc.subject.none.fl_str_mv LEMNISCATES
PLANAR MEASURE
INEQUALITIES
topic LEMNISCATES
PLANAR MEASURE
INEQUALITIES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper, we establish the following conjecture: There exists a constant K such that every lemniscate E(a,c), a Î C^n, c>0, contains a disk B(a, c) with mu(E(a, c)) £ Kmu(B(a, c)), where mu is the planar measure. We prove this conjecture for any family of lemniscates with at the most three foci and for any family of lemniscates where its foci satisfy a suitable condition.
Fil: Cuenya, Hector Hugo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; Argentina
Fil: Levis, Fabián Eduardo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
description In this paper, we establish the following conjecture: There exists a constant K such that every lemniscate E(a,c), a Î C^n, c>0, contains a disk B(a, c) with mu(E(a, c)) £ Kmu(B(a, c)), where mu is the planar measure. We prove this conjecture for any family of lemniscates with at the most three foci and for any family of lemniscates where its foci satisfy a suitable condition.
publishDate 2007
dc.date.none.fl_str_mv 2007-12
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/11336/242026
Cuenya, Hector Hugo; Levis, Fabián Eduardo; A property of the planar measure of the lemniscates; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 336; 2; 12-2007; 953-961
0022-247X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/242026
identifier_str_mv Cuenya, Hector Hugo; Levis, Fabián Eduardo; A property of the planar measure of the lemniscates; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 336; 2; 12-2007; 953-961
0022-247X
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://www.sciencedirect.com/science/article/pii/S0022247X07003319
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2007.03.034
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 Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
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 13.176822

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