The structure of weakly stable minimal hypersurfaces

Detalhes bibliográficos
Autor(a) principal: Cheng,Xu
Data de Publicação: 2006
Outros Autores: Cheung,Leung-Fu, Zhou,Detang
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=S0001-37652006000200001
Resumo: In this short communication, we announce results from our research on the structure of complete noncompact oriented weakly stable minimal hypersurfaces in a manifold of nonnegative sectional curvature. In particular, a complete oriented weakly stable minimal hypersurface in Rm, m > 4, must have only one end; any complete noncompact oriented weakly stable minimal hypersurface has only one end if the complete oriented ambient manifold Nm, m > 7, has nonnegative sectional curvature and Ricci curvature bounded below by a positive constant; a complete oriented weakly stable minimal hypersurface in Rm, m > 4, with finite total scalar curvature is a hyperplane.
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spelling The structure of weakly stable minimal hypersurfacesminimal hypersurfacesweak stabilityendsIn this short communication, we announce results from our research on the structure of complete noncompact oriented weakly stable minimal hypersurfaces in a manifold of nonnegative sectional curvature. In particular, a complete oriented weakly stable minimal hypersurface in Rm, m > 4, must have only one end; any complete noncompact oriented weakly stable minimal hypersurface has only one end if the complete oriented ambient manifold Nm, m > 7, has nonnegative sectional curvature and Ricci curvature bounded below by a positive constant; a complete oriented weakly stable minimal hypersurface in Rm, m > 4, with finite total scalar curvature is a hyperplane.Academia Brasileira de Ciências2006-06-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652006000200001Anais da Academia Brasileira de Ciências v.78 n.2 2006reponame:Anais da Academia Brasileira de Ciências (Online)instname:Academia Brasileira de Ciências (ABC)instacron:ABC10.1590/S0001-37652006000200001info:eu-repo/semantics/openAccessCheng,XuCheung,Leung-FuZhou,Detangeng2006-05-11T00:00:00Zoai:scielo:S0001-37652006000200001Revistahttp://www.scielo.br/aabchttps://old.scielo.br/oai/scielo-oai.php||aabc@abc.org.br1678-26900001-3765opendoar:2006-05-11T00:00Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)false
dc.title.none.fl_str_mv The structure of weakly stable minimal hypersurfaces
title The structure of weakly stable minimal hypersurfaces
spellingShingle The structure of weakly stable minimal hypersurfaces
Cheng,Xu
minimal hypersurfaces
weak stability
ends
title_short The structure of weakly stable minimal hypersurfaces
title_full The structure of weakly stable minimal hypersurfaces
title_fullStr The structure of weakly stable minimal hypersurfaces
title_full_unstemmed The structure of weakly stable minimal hypersurfaces
title_sort The structure of weakly stable minimal hypersurfaces
author Cheng,Xu
author_facet Cheng,Xu
Cheung,Leung-Fu
Zhou,Detang
author_role author
author2 Cheung,Leung-Fu
Zhou,Detang
author2_role author
author
dc.contributor.author.fl_str_mv Cheng,Xu
Cheung,Leung-Fu
Zhou,Detang
dc.subject.por.fl_str_mv minimal hypersurfaces
weak stability
ends
topic minimal hypersurfaces
weak stability
ends
description In this short communication, we announce results from our research on the structure of complete noncompact oriented weakly stable minimal hypersurfaces in a manifold of nonnegative sectional curvature. In particular, a complete oriented weakly stable minimal hypersurface in Rm, m > 4, must have only one end; any complete noncompact oriented weakly stable minimal hypersurface has only one end if the complete oriented ambient manifold Nm, m > 7, has nonnegative sectional curvature and Ricci curvature bounded below by a positive constant; a complete oriented weakly stable minimal hypersurface in Rm, m > 4, with finite total scalar curvature is a hyperplane.
publishDate 2006
dc.date.none.fl_str_mv 2006-06-01
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=S0001-37652006000200001
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652006000200001
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0001-37652006000200001
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.78 n.2 2006
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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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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