Complete minimal surfaces and harmonic functions

We prove that for any open Riemann surface N and any non constant harmonic function h : N → R, there exists a complete conformal minimal immersion X : N → R3 whose third coordinate function coincides with h. As a consequence, completeminimal surfaceswith arbitrary conformal structure andwhose Gauss...

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Authors: Alarcón, Antonio, Fernández Delgado, Isabel, López, Francisco J.
Format: article
Status:Versión enviada para evaluación y publicación
Publication Date:2012
Country:España
Institution:Universidad de Sevilla (US)
Repository:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/93403
Online Access:https://hdl.handle.net/11441/93403
https://doi.org/10.4171/CMH/272
Access Level:Open access
Keyword:Complete minimal surfaces
Harmonic functions on Riemann surfaces
Gauss map
Holomorphic immersion
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spelling Complete minimal surfaces and harmonic functionsAlarcón, AntonioFernández Delgado, IsabelLópez, Francisco J.Complete minimal surfacesHarmonic functions on Riemann surfacesGauss mapHolomorphic immersionWe prove that for any open Riemann surface N and any non constant harmonic function h : N → R, there exists a complete conformal minimal immersion X : N → R3 whose third coordinate function coincides with h. As a consequence, completeminimal surfaceswith arbitrary conformal structure andwhose Gauss map misses two points are constructed.Ministerio de Educación y Ciencia MTM2007-61775Ministerio de Educación y Ciencia MTM2007-64504Junta de Andalucía P06-FQM-01642.European Mathematical SocietyMatemática Aplicada I2012info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/93403https://doi.org/10.4171/CMH/272reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésCommentarii Mathematici Helvetici, 87 (4), 891-904.MTM2007-61775MTM2007-64504P06-FQM-01642.https://www.ems-ph.org/journals/show_abstract.php?issn=0010-2571&vol=87&iss=4&rank=5info:eu-repo/semantics/openAccessoai:idus.us.es:11441/934032026-06-17T12:51:07Z
dc.title.none.fl_str_mv Complete minimal surfaces and harmonic functions
title Complete minimal surfaces and harmonic functions
spellingShingle Complete minimal surfaces and harmonic functions
Alarcón, Antonio
Complete minimal surfaces
Harmonic functions on Riemann surfaces
Gauss map
Holomorphic immersion
title_short Complete minimal surfaces and harmonic functions
title_full Complete minimal surfaces and harmonic functions
title_fullStr Complete minimal surfaces and harmonic functions
title_full_unstemmed Complete minimal surfaces and harmonic functions
title_sort Complete minimal surfaces and harmonic functions
dc.creator.none.fl_str_mv Alarcón, Antonio
Fernández Delgado, Isabel
López, Francisco J.
author Alarcón, Antonio
author_facet Alarcón, Antonio
Fernández Delgado, Isabel
López, Francisco J.
author_role author
author2 Fernández Delgado, Isabel
López, Francisco J.
author2_role author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
dc.subject.none.fl_str_mv Complete minimal surfaces
Harmonic functions on Riemann surfaces
Gauss map
Holomorphic immersion
topic Complete minimal surfaces
Harmonic functions on Riemann surfaces
Gauss map
Holomorphic immersion
description We prove that for any open Riemann surface N and any non constant harmonic function h : N → R, there exists a complete conformal minimal immersion X : N → R3 whose third coordinate function coincides with h. As a consequence, completeminimal surfaceswith arbitrary conformal structure andwhose Gauss map misses two points are constructed.
publishDate 2012
dc.date.none.fl_str_mv 2012
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/93403
https://doi.org/10.4171/CMH/272
url https://hdl.handle.net/11441/93403
https://doi.org/10.4171/CMH/272
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Commentarii Mathematici Helvetici, 87 (4), 891-904.
MTM2007-61775
MTM2007-64504
P06-FQM-01642.
https://www.ems-ph.org/journals/show_abstract.php?issn=0010-2571&vol=87&iss=4&rank=5
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv European Mathematical Society
publisher.none.fl_str_mv European Mathematical Society
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869409388196790272
score 15.300719

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