A PDE Approach to the Existence and Regularity of Surfaces of Minimum Mean Curvature Variation

Autores
Caffarelli, Luis A.; Stinga, Pablo Raul; Vivas, Hernán Agustín
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We develop an analytic theory of existence and regularity of surfaces (given by graphs) arising from the geometric minimization problem min M 1 2 ˆ M |∇MH| 2 dA where M ranges over all n-dimensional manifolds in R n+1 with prescribed boundary, ∇MH is the tangential gradient along M of the mean curvature H of M and dA is the differential of surface area. The minimizers, called surfaces of minimum mean curvature variation, are central in applications of computer-aided design, computer-aided manufacturing and mechanics. Our main results show the existence of both smooth surfaces and of variational solutions to the minimization problem together with geometric regularity results in the case of graphs. These are the first analytic results available on the literature for this problem.
Fil: Caffarelli, Luis A.. University of Texas at Austin; Estados Unidos
Fil: Stinga, Pablo Raul. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Iowa State University; Estados Unidos
Fil: Vivas, Hernán Agustín. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Mar del Plata. Facultad de Cs.exactas y Naturales. Centro Marplatense de Investigaciones Matematicas.; Argentina
Materia
DIFFERENTIAL GEOMETRY
SURFACES OF MINIMUM CURVATURE VARIATON
MINIMAL SURFACES
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:11336/275841
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A PDE Approach to the Existence and Regularity of Surfaces of Minimum Mean Curvature VariationCaffarelli, Luis A.Stinga, Pablo RaulVivas, Hernán AgustínDIFFERENTIAL GEOMETRYSURFACES OF MINIMUM CURVATURE VARIATONMINIMAL SURFACEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We develop an analytic theory of existence and regularity of surfaces (given by graphs) arising from the geometric minimization problem min M 1 2 ˆ M |∇MH| 2 dA where M ranges over all n-dimensional manifolds in R n+1 with prescribed boundary, ∇MH is the tangential gradient along M of the mean curvature H of M and dA is the differential of surface area. The minimizers, called surfaces of minimum mean curvature variation, are central in applications of computer-aided design, computer-aided manufacturing and mechanics. Our main results show the existence of both smooth surfaces and of variational solutions to the minimization problem together with geometric regularity results in the case of graphs. These are the first analytic results available on the literature for this problem.Fil: Caffarelli, Luis A.. University of Texas at Austin; Estados UnidosFil: Stinga, Pablo Raul. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Iowa State University; Estados UnidosFil: Vivas, Hernán Agustín. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Mar del Plata. Facultad de Cs.exactas y Naturales. Centro Marplatense de Investigaciones Matematicas.; ArgentinaSpringer2024-08info: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/11336/275841Caffarelli, Luis A.; Stinga, Pablo Raul; Vivas, Hernán Agustín; A PDE Approach to the Existence and Regularity of Surfaces of Minimum Mean Curvature Variation; Springer; Archive For Rational Mechanics And Analysis; 248; 5; 8-2024; 1-130003-9527CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00205-024-02016-5info:eu-repo/semantics/altIdentifier/doi/10.1007/s00205-024-02016-5info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2301.00082info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-12-23T13:38:05Zoai:ri.conicet.gov.ar:11336/275841instacron: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:34982025-12-23 13:38:05.407CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A PDE Approach to the Existence and Regularity of Surfaces of Minimum Mean Curvature Variation
title A PDE Approach to the Existence and Regularity of Surfaces of Minimum Mean Curvature Variation
spellingShingle A PDE Approach to the Existence and Regularity of Surfaces of Minimum Mean Curvature Variation
Caffarelli, Luis A.
DIFFERENTIAL GEOMETRY
SURFACES OF MINIMUM CURVATURE VARIATON
MINIMAL SURFACES
title_short A PDE Approach to the Existence and Regularity of Surfaces of Minimum Mean Curvature Variation
title_full A PDE Approach to the Existence and Regularity of Surfaces of Minimum Mean Curvature Variation
title_fullStr A PDE Approach to the Existence and Regularity of Surfaces of Minimum Mean Curvature Variation
title_full_unstemmed A PDE Approach to the Existence and Regularity of Surfaces of Minimum Mean Curvature Variation
title_sort A PDE Approach to the Existence and Regularity of Surfaces of Minimum Mean Curvature Variation
dc.creator.none.fl_str_mv Caffarelli, Luis A.
Stinga, Pablo Raul
Vivas, Hernán Agustín
author Caffarelli, Luis A.
author_facet Caffarelli, Luis A.
Stinga, Pablo Raul
Vivas, Hernán Agustín
author_role author
author2 Stinga, Pablo Raul
Vivas, Hernán Agustín
author2_role author
author
dc.subject.none.fl_str_mv DIFFERENTIAL GEOMETRY
SURFACES OF MINIMUM CURVATURE VARIATON
MINIMAL SURFACES
topic DIFFERENTIAL GEOMETRY
SURFACES OF MINIMUM CURVATURE VARIATON
MINIMAL SURFACES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We develop an analytic theory of existence and regularity of surfaces (given by graphs) arising from the geometric minimization problem min M 1 2 ˆ M |∇MH| 2 dA where M ranges over all n-dimensional manifolds in R n+1 with prescribed boundary, ∇MH is the tangential gradient along M of the mean curvature H of M and dA is the differential of surface area. The minimizers, called surfaces of minimum mean curvature variation, are central in applications of computer-aided design, computer-aided manufacturing and mechanics. Our main results show the existence of both smooth surfaces and of variational solutions to the minimization problem together with geometric regularity results in the case of graphs. These are the first analytic results available on the literature for this problem.
Fil: Caffarelli, Luis A.. University of Texas at Austin; Estados Unidos
Fil: Stinga, Pablo Raul. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Iowa State University; Estados Unidos
Fil: Vivas, Hernán Agustín. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Mar del Plata. Facultad de Cs.exactas y Naturales. Centro Marplatense de Investigaciones Matematicas.; Argentina
description We develop an analytic theory of existence and regularity of surfaces (given by graphs) arising from the geometric minimization problem min M 1 2 ˆ M |∇MH| 2 dA where M ranges over all n-dimensional manifolds in R n+1 with prescribed boundary, ∇MH is the tangential gradient along M of the mean curvature H of M and dA is the differential of surface area. The minimizers, called surfaces of minimum mean curvature variation, are central in applications of computer-aided design, computer-aided manufacturing and mechanics. Our main results show the existence of both smooth surfaces and of variational solutions to the minimization problem together with geometric regularity results in the case of graphs. These are the first analytic results available on the literature for this problem.
publishDate 2024
dc.date.none.fl_str_mv 2024-08
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/11336/275841
Caffarelli, Luis A.; Stinga, Pablo Raul; Vivas, Hernán Agustín; A PDE Approach to the Existence and Regularity of Surfaces of Minimum Mean Curvature Variation; Springer; Archive For Rational Mechanics And Analysis; 248; 5; 8-2024; 1-13
0003-9527
CONICET Digital
CONICET
url http://hdl.handle.net/11336/275841
identifier_str_mv Caffarelli, Luis A.; Stinga, Pablo Raul; Vivas, Hernán Agustín; A PDE Approach to the Existence and Regularity of Surfaces of Minimum Mean Curvature Variation; Springer; Archive For Rational Mechanics And Analysis; 248; 5; 8-2024; 1-13
0003-9527
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/s00205-024-02016-5
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00205-024-02016-5
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2301.00082
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 12.952241

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