Graphs with constant mean curvature in the 3-hyperbolic space
Autor(a) principal: | |
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Data de Publicação: | 2002 |
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=S0001-37652002000300001 |
Resumo: | In this work we will deal with disc type surfaces of constant mean curvature in the three dimensional hyperbolic space which are given as graphs of smooth functions over planar domains. From the various types of graphs that could be defined in the hyperbolic space we consider in particular the horizontal and the geodesic graphs. We proved that if the mean curvature is constant, then such graphs are equivalent in the following sense: suppose that M is a constant mean curvature surface in the 3-hyperbolic space such that M is a geodesic graph of a function rho that is zero at the boundary, then there exist a smooth function f that also vanishes at the boundary, such that M is a horizontal graph of f. Moreover, the reciprocal is also true. |
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Anais da Academia Brasileira de Ciências (Online) |
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Graphs with constant mean curvature in the 3-hyperbolic spacehyperbolic spacegeodesic and horizontal graphsconstant mean curvatureelliptic partial differential equationsIn this work we will deal with disc type surfaces of constant mean curvature in the three dimensional hyperbolic space which are given as graphs of smooth functions over planar domains. From the various types of graphs that could be defined in the hyperbolic space we consider in particular the horizontal and the geodesic graphs. We proved that if the mean curvature is constant, then such graphs are equivalent in the following sense: suppose that M is a constant mean curvature surface in the 3-hyperbolic space such that M is a geodesic graph of a function rho that is zero at the boundary, then there exist a smooth function f that also vanishes at the boundary, such that M is a horizontal graph of f. Moreover, the reciprocal is also true.Academia Brasileira de Ciências2002-09-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652002000300001Anais da Academia Brasileira de Ciências v.74 n.3 2002reponame:Anais da Academia Brasileira de Ciências (Online)instname:Academia Brasileira de Ciências (ABC)instacron:ABC10.1590/S0001-37652002000300001info:eu-repo/semantics/openAccessHINOJOSA,PEDRO A.eng2002-10-09T00:00:00Zoai:scielo:S0001-37652002000300001Revistahttp://www.scielo.br/aabchttps://old.scielo.br/oai/scielo-oai.php||aabc@abc.org.br1678-26900001-3765opendoar:2002-10-09T00:00Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)false |
dc.title.none.fl_str_mv |
Graphs with constant mean curvature in the 3-hyperbolic space |
title |
Graphs with constant mean curvature in the 3-hyperbolic space |
spellingShingle |
Graphs with constant mean curvature in the 3-hyperbolic space HINOJOSA,PEDRO A. hyperbolic space geodesic and horizontal graphs constant mean curvature elliptic partial differential equations |
title_short |
Graphs with constant mean curvature in the 3-hyperbolic space |
title_full |
Graphs with constant mean curvature in the 3-hyperbolic space |
title_fullStr |
Graphs with constant mean curvature in the 3-hyperbolic space |
title_full_unstemmed |
Graphs with constant mean curvature in the 3-hyperbolic space |
title_sort |
Graphs with constant mean curvature in the 3-hyperbolic space |
author |
HINOJOSA,PEDRO A. |
author_facet |
HINOJOSA,PEDRO A. |
author_role |
author |
dc.contributor.author.fl_str_mv |
HINOJOSA,PEDRO A. |
dc.subject.por.fl_str_mv |
hyperbolic space geodesic and horizontal graphs constant mean curvature elliptic partial differential equations |
topic |
hyperbolic space geodesic and horizontal graphs constant mean curvature elliptic partial differential equations |
description |
In this work we will deal with disc type surfaces of constant mean curvature in the three dimensional hyperbolic space which are given as graphs of smooth functions over planar domains. From the various types of graphs that could be defined in the hyperbolic space we consider in particular the horizontal and the geodesic graphs. We proved that if the mean curvature is constant, then such graphs are equivalent in the following sense: suppose that M is a constant mean curvature surface in the 3-hyperbolic space such that M is a geodesic graph of a function rho that is zero at the boundary, then there exist a smooth function f that also vanishes at the boundary, such that M is a horizontal graph of f. Moreover, the reciprocal is also true. |
publishDate |
2002 |
dc.date.none.fl_str_mv |
2002-09-01 |
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=S0001-37652002000300001 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652002000300001 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/S0001-37652002000300001 |
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.74 n.3 2002 reponame:Anais da Academia Brasileira de Ciências (Online) instname:Academia Brasileira de Ciências (ABC) instacron:ABC |
instname_str |
Academia Brasileira de Ciências (ABC) |
instacron_str |
ABC |
institution |
ABC |
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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1754302855766867968 |