The Bernstein problem for elliptic Weingarten multigraphs

We prove that any complete, uniformly ellipticWeingarten surface in Euclidean 3-space whose Gauss map image omits an open hemisphere is a cylinder or a plane. This generalizes a classical theorem by Hoffman, Osserman and Schoen for constant mean curvature surfaces. In particular, this proves that pl...

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Detalles Bibliográficos
Autores: Fernández Delgado, Isabel, Gálvez, José A., Mira, Pablo
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2020
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/115305
Acceso en línea:https://hdl.handle.net/11441/115305
Access Level:acceso abierto
Palabra clave:Weingarten surfaces
Fully nonlinear elliptic equations
Bernstein problem
Multigraphs
Curvature estimates
Quasiconformal Gauss map
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spelling The Bernstein problem for elliptic Weingarten multigraphsFernández Delgado, IsabelGálvez, José A.Mira, PabloWeingarten surfacesFully nonlinear elliptic equationsBernstein problemMultigraphsCurvature estimatesQuasiconformal Gauss mapWe prove that any complete, uniformly ellipticWeingarten surface in Euclidean 3-space whose Gauss map image omits an open hemisphere is a cylinder or a plane. This generalizes a classical theorem by Hoffman, Osserman and Schoen for constant mean curvature surfaces. In particular, this proves that planes are the only complete, uniformly elliptic Weingarten multigraphs. We also show that this result holds for a large class of non-uniformly elliptic Weingarten equations. In particular, this solves in the affirmative the Bernstein problem for entire graphs for that class of elliptic equations.Ministerio de Economía y Competitividad MTM2016-80313-PCornell UniversityMatemática Aplicada IMinisterio de Economía y Competitividad (MINECO). España2020info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/115305reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésArXiv.org, arXiv:2004.08275v1, 1-24.MTM2016-80313-Phttps://arxiv.org//abs/2004.08275v1info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1153052026-06-17T12:51:07Z
dc.title.none.fl_str_mv The Bernstein problem for elliptic Weingarten multigraphs
title The Bernstein problem for elliptic Weingarten multigraphs
spellingShingle The Bernstein problem for elliptic Weingarten multigraphs
Fernández Delgado, Isabel
Weingarten surfaces
Fully nonlinear elliptic equations
Bernstein problem
Multigraphs
Curvature estimates
Quasiconformal Gauss map
title_short The Bernstein problem for elliptic Weingarten multigraphs
title_full The Bernstein problem for elliptic Weingarten multigraphs
title_fullStr The Bernstein problem for elliptic Weingarten multigraphs
title_full_unstemmed The Bernstein problem for elliptic Weingarten multigraphs
title_sort The Bernstein problem for elliptic Weingarten multigraphs
dc.creator.none.fl_str_mv Fernández Delgado, Isabel
Gálvez, José A.
Mira, Pablo
author Fernández Delgado, Isabel
author_facet Fernández Delgado, Isabel
Gálvez, José A.
Mira, Pablo
author_role author
author2 Gálvez, José A.
Mira, Pablo
author2_role author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
Ministerio de Economía y Competitividad (MINECO). España
dc.subject.none.fl_str_mv Weingarten surfaces
Fully nonlinear elliptic equations
Bernstein problem
Multigraphs
Curvature estimates
Quasiconformal Gauss map
topic Weingarten surfaces
Fully nonlinear elliptic equations
Bernstein problem
Multigraphs
Curvature estimates
Quasiconformal Gauss map
description We prove that any complete, uniformly ellipticWeingarten surface in Euclidean 3-space whose Gauss map image omits an open hemisphere is a cylinder or a plane. This generalizes a classical theorem by Hoffman, Osserman and Schoen for constant mean curvature surfaces. In particular, this proves that planes are the only complete, uniformly elliptic Weingarten multigraphs. We also show that this result holds for a large class of non-uniformly elliptic Weingarten equations. In particular, this solves in the affirmative the Bernstein problem for entire graphs for that class of elliptic equations.
publishDate 2020
dc.date.none.fl_str_mv 2020
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/115305
url https://hdl.handle.net/11441/115305
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv ArXiv.org, arXiv:2004.08275v1, 1-24.
MTM2016-80313-P
https://arxiv.org//abs/2004.08275v1
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 Cornell University
publisher.none.fl_str_mv Cornell University
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
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