Embedded positive constant r-mean curvature hypersurfaces in Mm × R

Detalhes bibliográficos
Autor(a) principal: Cheng,Xu
Data de Publicação: 2005
Outros Autores: Rosenberg,Harold
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=S0001-37652005000200001
Resumo: Let M be an m-dimensional Riemannian manifold with sectional curvature bounded from below. We consider hypersurfaces in the (m + 1)-dimensional product manifold M × R with positive constant r-mean curvature. We obtain height estimates of certain compact vertical graphs in M × R with boundary in M × {0}. We apply this to obtain topological obstructions for the existence of some hypersurfaces. We also discuss the rotational symmetry of some embedded complete surfaces in S² × R of positive constant 2-mean curvature.
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spelling Embedded positive constant r-mean curvature hypersurfaces in Mm × Rproduct manifoldhypersurfacer-mean curvatureLet M be an m-dimensional Riemannian manifold with sectional curvature bounded from below. We consider hypersurfaces in the (m + 1)-dimensional product manifold M × R with positive constant r-mean curvature. We obtain height estimates of certain compact vertical graphs in M × R with boundary in M × {0}. We apply this to obtain topological obstructions for the existence of some hypersurfaces. We also discuss the rotational symmetry of some embedded complete surfaces in S² × R of positive constant 2-mean curvature.Academia Brasileira de Ciências2005-06-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652005000200001Anais da Academia Brasileira de Ciências v.77 n.2 2005reponame:Anais da Academia Brasileira de Ciências (Online)instname:Academia Brasileira de Ciências (ABC)instacron:ABC10.1590/S0001-37652005000200001info:eu-repo/semantics/openAccessCheng,XuRosenberg,Haroldeng2005-05-09T00:00:00Zoai:scielo:S0001-37652005000200001Revistahttp://www.scielo.br/aabchttps://old.scielo.br/oai/scielo-oai.php||aabc@abc.org.br1678-26900001-3765opendoar:2005-05-09T00:00Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)false
dc.title.none.fl_str_mv Embedded positive constant r-mean curvature hypersurfaces in Mm × R
title Embedded positive constant r-mean curvature hypersurfaces in Mm × R
spellingShingle Embedded positive constant r-mean curvature hypersurfaces in Mm × R
Cheng,Xu
product manifold
hypersurface
r-mean curvature
title_short Embedded positive constant r-mean curvature hypersurfaces in Mm × R
title_full Embedded positive constant r-mean curvature hypersurfaces in Mm × R
title_fullStr Embedded positive constant r-mean curvature hypersurfaces in Mm × R
title_full_unstemmed Embedded positive constant r-mean curvature hypersurfaces in Mm × R
title_sort Embedded positive constant r-mean curvature hypersurfaces in Mm × R
author Cheng,Xu
author_facet Cheng,Xu
Rosenberg,Harold
author_role author
author2 Rosenberg,Harold
author2_role author
dc.contributor.author.fl_str_mv Cheng,Xu
Rosenberg,Harold
dc.subject.por.fl_str_mv product manifold
hypersurface
r-mean curvature
topic product manifold
hypersurface
r-mean curvature
description Let M be an m-dimensional Riemannian manifold with sectional curvature bounded from below. We consider hypersurfaces in the (m + 1)-dimensional product manifold M × R with positive constant r-mean curvature. We obtain height estimates of certain compact vertical graphs in M × R with boundary in M × {0}. We apply this to obtain topological obstructions for the existence of some hypersurfaces. We also discuss the rotational symmetry of some embedded complete surfaces in S² × R of positive constant 2-mean curvature.
publishDate 2005
dc.date.none.fl_str_mv 2005-06-01
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=S0001-37652005000200001
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652005000200001
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0001-37652005000200001
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.77 n.2 2005
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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