A duality result between the minimal surface equation and the maximal surface equation

Detalhes bibliográficos
Autor(a) principal: ALÍAS,LUIS J.
Data de Publicação: 2001
Outros Autores: PALMER,BENNETT
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Anais da Academia Brasileira de Ciências (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652001000200002
Resumo: In this note we show how classical Bernstein's theorem on minimal surfaces in the Euclidean space can be seen as a consequence of Calabi-Bernstein's theorem on maximal surfaces in the Lorentz-Minkowski space (and viceversa). This follows from a simple but nice duality between solutions to their corresponding differential equations.
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spelling A duality result between the minimal surface equation and the maximal surface equationMinimal surface equationMaximal surface equationBernstein's theoremCalabi-Bernstein's theoremIn this note we show how classical Bernstein's theorem on minimal surfaces in the Euclidean space can be seen as a consequence of Calabi-Bernstein's theorem on maximal surfaces in the Lorentz-Minkowski space (and viceversa). This follows from a simple but nice duality between solutions to their corresponding differential equations.Academia Brasileira de Ciências2001-06-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652001000200002Anais da Academia Brasileira de Ciências v.73 n.2 2001reponame:Anais da Academia Brasileira de Ciências (Online)instname:Academia Brasileira de Ciências (ABC)instacron:ABC10.1590/S0001-37652001000200002info:eu-repo/semantics/openAccessALÍAS,LUIS J.PALMER,BENNETTeng2001-06-08T00:00:00Zoai:scielo:S0001-37652001000200002Revistahttp://www.scielo.br/aabchttps://old.scielo.br/oai/scielo-oai.php||aabc@abc.org.br1678-26900001-3765opendoar:2001-06-08T00:00Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)false
dc.title.none.fl_str_mv A duality result between the minimal surface equation and the maximal surface equation
title A duality result between the minimal surface equation and the maximal surface equation
spellingShingle A duality result between the minimal surface equation and the maximal surface equation
ALÍAS,LUIS J.
Minimal surface equation
Maximal surface equation
Bernstein's theorem
Calabi-Bernstein's theorem
title_short A duality result between the minimal surface equation and the maximal surface equation
title_full A duality result between the minimal surface equation and the maximal surface equation
title_fullStr A duality result between the minimal surface equation and the maximal surface equation
title_full_unstemmed A duality result between the minimal surface equation and the maximal surface equation
title_sort A duality result between the minimal surface equation and the maximal surface equation
author ALÍAS,LUIS J.
author_facet ALÍAS,LUIS J.
PALMER,BENNETT
author_role author
author2 PALMER,BENNETT
author2_role author
dc.contributor.author.fl_str_mv ALÍAS,LUIS J.
PALMER,BENNETT
dc.subject.por.fl_str_mv Minimal surface equation
Maximal surface equation
Bernstein's theorem
Calabi-Bernstein's theorem
topic Minimal surface equation
Maximal surface equation
Bernstein's theorem
Calabi-Bernstein's theorem
description In this note we show how classical Bernstein's theorem on minimal surfaces in the Euclidean space can be seen as a consequence of Calabi-Bernstein's theorem on maximal surfaces in the Lorentz-Minkowski space (and viceversa). This follows from a simple but nice duality between solutions to their corresponding differential equations.
publishDate 2001
dc.date.none.fl_str_mv 2001-06-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652001000200002
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652001000200002
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0001-37652001000200002
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Academia Brasileira de Ciências
publisher.none.fl_str_mv Academia Brasileira de Ciências
dc.source.none.fl_str_mv Anais da Academia Brasileira de Ciências v.73 n.2 2001
reponame:Anais da Academia Brasileira de Ciências (Online)
instname:Academia Brasileira de Ciências (ABC)
instacron:ABC
instname_str Academia Brasileira de Ciências (ABC)
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reponame_str Anais da Academia Brasileira de Ciências (Online)
collection Anais da Academia Brasileira de Ciências (Online)
repository.name.fl_str_mv Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)
repository.mail.fl_str_mv ||aabc@abc.org.br
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