Realization of Bipartite Weighted Graphs by Stable Gauss Maps

[EN] The singularities of a stable Gauss map of a closed orientable surface immersed generically in three-dimensional Euclidean space, according to H. Whitney¿s Theorem, are of the fold and cusp types. The singular set of a stable Gauss map of a surface, which consists of curves of fold points conta...

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Autores: Evangelista Neves, Thiago, Mendes de Jesus, Catarina, Sanabria-Codesal, Esther|||0000-0002-4523-1991
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/222655
Acceso en línea:https://riunet.upv.es/handle/10251/222655
Access Level:acceso abierto
Palabra clave:Stable Gauss maps
Bipartite weighted graphs
Singularities
Parabolic curves
Euclidean space
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spelling Realization of Bipartite Weighted Graphs by Stable Gauss MapsEvangelista Neves, ThiagoMendes de Jesus, CatarinaSanabria-Codesal, Esther|||0000-0002-4523-1991Stable Gauss mapsBipartite weighted graphsSingularitiesParabolic curvesEuclidean space[EN] The singularities of a stable Gauss map of a closed orientable surface immersed generically in three-dimensional Euclidean space, according to H. Whitney¿s Theorem, are of the fold and cusp types. The singular set of a stable Gauss map of a surface, which consists of curves of fold points containing isolated cusp points, is the parabolic set on the surface. Each parabolic curve of the singular set separates a hyperbolic region from an elliptic region of the surface. In this work, we will explore how weighted graphs can be associated with stable Gauss maps and present a general result that determines necessary and sufficient conditions for a weighted graph to be associated with a stable Gauss map.Sociedade Brasileira de Matemática Aplicada e ComputacionalDepartamento de Matemática AplicadaEscuela Técnica Superior de Ingeniería Aeroespacial y Diseño IndustrialEuropean CommissionEuropean Regional Development FundUniversitat Politècnica de ValènciaRepositorio Institucional de la Universitat Politècnica de València Riunet20252025-01-20journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/222655reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023 PID2021-124577NB-I00 SINGULARIDADES, GEOMETRIA GENERICA Y APLICACIONESopen accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/2226552026-06-13T07:49:27Z
dc.title.none.fl_str_mv Realization of Bipartite Weighted Graphs by Stable Gauss Maps
title Realization of Bipartite Weighted Graphs by Stable Gauss Maps
spellingShingle Realization of Bipartite Weighted Graphs by Stable Gauss Maps
Evangelista Neves, Thiago
Stable Gauss maps
Bipartite weighted graphs
Singularities
Parabolic curves
Euclidean space
title_short Realization of Bipartite Weighted Graphs by Stable Gauss Maps
title_full Realization of Bipartite Weighted Graphs by Stable Gauss Maps
title_fullStr Realization of Bipartite Weighted Graphs by Stable Gauss Maps
title_full_unstemmed Realization of Bipartite Weighted Graphs by Stable Gauss Maps
title_sort Realization of Bipartite Weighted Graphs by Stable Gauss Maps
dc.creator.none.fl_str_mv Evangelista Neves, Thiago
Mendes de Jesus, Catarina
Sanabria-Codesal, Esther|||0000-0002-4523-1991
author Evangelista Neves, Thiago
author_facet Evangelista Neves, Thiago
Mendes de Jesus, Catarina
Sanabria-Codesal, Esther|||0000-0002-4523-1991
author_role author
author2 Mendes de Jesus, Catarina
Sanabria-Codesal, Esther|||0000-0002-4523-1991
author2_role author
author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Escuela Técnica Superior de Ingeniería Aeroespacial y Diseño Industrial
European Commission
European Regional Development Fund
Universitat Politècnica de València
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Stable Gauss maps
Bipartite weighted graphs
Singularities
Parabolic curves
Euclidean space
topic Stable Gauss maps
Bipartite weighted graphs
Singularities
Parabolic curves
Euclidean space
description [EN] The singularities of a stable Gauss map of a closed orientable surface immersed generically in three-dimensional Euclidean space, according to H. Whitney¿s Theorem, are of the fold and cusp types. The singular set of a stable Gauss map of a surface, which consists of curves of fold points containing isolated cusp points, is the parabolic set on the surface. Each parabolic curve of the singular set separates a hyperbolic region from an elliptic region of the surface. In this work, we will explore how weighted graphs can be associated with stable Gauss maps and present a general result that determines necessary and sufficient conditions for a weighted graph to be associated with a stable Gauss map.
publishDate 2025
dc.date.none.fl_str_mv 2025
2025-01-20
dc.type.none.fl_str_mv journal 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://riunet.upv.es/handle/10251/222655
url https://riunet.upv.es/handle/10251/222655
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023 PID2021-124577NB-I00 SINGULARIDADES, GEOMETRIA GENERICA Y APLICACIONES
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
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
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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