The isoperimetric problem for lens spaces
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFMG |
Texto Completo: | https://doi.org/10.1007/s00208-018-1792-7 http://hdl.handle.net/1843/37087 |
Resumo: | We solve the isoperimetric problem in the lens spaces with large fundamental group. Namely, we prove that the isoperimetric surfaces are either geodesic spheres or quotients of Clifford tori. We also show that the isoperimetric problem in the lens spaces L(3, 1) and L(3, 2) follows from the proof of the Willmore conjecture by Marques and Neves. |
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2021-07-28T22:22:23Z2021-07-28T22:22:23Z2019374475497https://doi.org/10.1007/s00208-018-1792-71432-1807http://hdl.handle.net/1843/37087ttps://orcid.org/0000-0001-5626-4169We solve the isoperimetric problem in the lens spaces with large fundamental group. Namely, we prove that the isoperimetric surfaces are either geodesic spheres or quotients of Clifford tori. We also show that the isoperimetric problem in the lens spaces L(3, 1) and L(3, 2) follows from the proof of the Willmore conjecture by Marques and Neves.Resolvemos o problema isoperimétrico nos espaços da lente com grande grupo fundamental. Nomeadamente, provamos que as superfícies isoperimétricas são esferas geodésicas ou quocientes de toros de Clifford. Mostramos também que o problema isoperimétrico nos espaços de lente L (3, 1) e L (3, 2) decorre da prova da conjectura de Willmore por Marques e Neves.engUniversidade Federal de Minas GeraisUFMGBrasilICX - DEPARTAMENTO DE MATEMÁTICAMathematische AnnalenCálculo das variaçõesGeometria diferencialVariedade RiemannianaIsoperimetric problemDifferential geometryRiemannian manifoldThe isoperimetric problem for lens spacesO problema isoperimétrico para espaços de lentesinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttps://link.springer.com/article/10.1007/s00208-018-1792-7Celso Dos Santos Vianaapplication/pdfinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMGLICENSELicense.txtLicense.txttext/plain; charset=utf-82042https://repositorio.ufmg.br/bitstream/1843/37087/1/License.txtfa505098d172de0bc8864fc1287ffe22MD51ORIGINALMAT _ Viana Celso _ The isoperimetric problem for lens spaces _ 2018.pdfMAT _ Viana Celso _ The isoperimetric problem for lens spaces _ 2018.pdfapplication/pdf14970707https://repositorio.ufmg.br/bitstream/1843/37087/2/MAT%20_%20Viana%20Celso%20_%20The%20isoperimetric%20problem%20for%20lens%20spaces%20_%202018.pdf4c4a5d70a76ef3184b4f4b7215c337c2MD521843/370872021-07-28 19:22:23.514oai:repositorio.ufmg.br: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Repositório de PublicaçõesPUBhttps://repositorio.ufmg.br/oaiopendoar:2021-07-28T22:22:23Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)false |
dc.title.pt_BR.fl_str_mv |
The isoperimetric problem for lens spaces |
dc.title.alternative.pt_BR.fl_str_mv |
O problema isoperimétrico para espaços de lentes |
title |
The isoperimetric problem for lens spaces |
spellingShingle |
The isoperimetric problem for lens spaces Celso Dos Santos Viana Isoperimetric problem Differential geometry Riemannian manifold Cálculo das variações Geometria diferencial Variedade Riemanniana |
title_short |
The isoperimetric problem for lens spaces |
title_full |
The isoperimetric problem for lens spaces |
title_fullStr |
The isoperimetric problem for lens spaces |
title_full_unstemmed |
The isoperimetric problem for lens spaces |
title_sort |
The isoperimetric problem for lens spaces |
author |
Celso Dos Santos Viana |
author_facet |
Celso Dos Santos Viana |
author_role |
author |
dc.contributor.author.fl_str_mv |
Celso Dos Santos Viana |
dc.subject.por.fl_str_mv |
Isoperimetric problem Differential geometry Riemannian manifold |
topic |
Isoperimetric problem Differential geometry Riemannian manifold Cálculo das variações Geometria diferencial Variedade Riemanniana |
dc.subject.other.pt_BR.fl_str_mv |
Cálculo das variações Geometria diferencial Variedade Riemanniana |
description |
We solve the isoperimetric problem in the lens spaces with large fundamental group. Namely, we prove that the isoperimetric surfaces are either geodesic spheres or quotients of Clifford tori. We also show that the isoperimetric problem in the lens spaces L(3, 1) and L(3, 2) follows from the proof of the Willmore conjecture by Marques and Neves. |
publishDate |
2019 |
dc.date.issued.fl_str_mv |
2019 |
dc.date.accessioned.fl_str_mv |
2021-07-28T22:22:23Z |
dc.date.available.fl_str_mv |
2021-07-28T22:22:23Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/1843/37087 |
dc.identifier.doi.pt_BR.fl_str_mv |
https://doi.org/10.1007/s00208-018-1792-7 |
dc.identifier.issn.pt_BR.fl_str_mv |
1432-1807 |
dc.identifier.orcid.pt_BR.fl_str_mv |
ttps://orcid.org/0000-0001-5626-4169 |
url |
https://doi.org/10.1007/s00208-018-1792-7 http://hdl.handle.net/1843/37087 |
identifier_str_mv |
1432-1807 ttps://orcid.org/0000-0001-5626-4169 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartof.pt_BR.fl_str_mv |
Mathematische Annalen |
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info:eu-repo/semantics/openAccess |
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openAccess |
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application/pdf |
dc.publisher.none.fl_str_mv |
Universidade Federal de Minas Gerais |
dc.publisher.initials.fl_str_mv |
UFMG |
dc.publisher.country.fl_str_mv |
Brasil |
dc.publisher.department.fl_str_mv |
ICX - DEPARTAMENTO DE MATEMÁTICA |
publisher.none.fl_str_mv |
Universidade Federal de Minas Gerais |
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