An elementary proof of MinVol(Rn) = 0 for n > 3

Detalhes bibliográficos
Autor(a) principal: Mei,Jiaqiang
Data de Publicação: 2008
Outros Autores: Wang,Hongyu, Xu,Haifeng
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=S0001-37652008000400002
Resumo: In this paper, we give an elementary proof of the result that the minimal volumes of R³ and R4 are zero. The approach is to construct a sequence of explicit complete metrics on them such that the sectional curvatures are bounded in absolute value by 1 and the volumes tend to zero. As a direct consequence, we get that MinVol (Rn) = 0 for n > 3.
id ABC-1_9e20cc3c9d763db4ec40bf8239b04bd0
oai_identifier_str oai:scielo:S0001-37652008000400002
network_acronym_str ABC-1
network_name_str Anais da Academia Brasileira de Ciências (Online)
repository_id_str
spelling An elementary proof of MinVol(Rn) = 0 for n > 3minimal volumesmooth gluingbounded geometryIn this paper, we give an elementary proof of the result that the minimal volumes of R³ and R4 are zero. The approach is to construct a sequence of explicit complete metrics on them such that the sectional curvatures are bounded in absolute value by 1 and the volumes tend to zero. As a direct consequence, we get that MinVol (Rn) = 0 for n > 3.Academia Brasileira de Ciências2008-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652008000400002Anais da Academia Brasileira de Ciências v.80 n.4 2008reponame:Anais da Academia Brasileira de Ciências (Online)instname:Academia Brasileira de Ciências (ABC)instacron:ABC10.1590/S0001-37652008000400002info:eu-repo/semantics/openAccessMei,JiaqiangWang,HongyuXu,Haifengeng2008-11-25T00:00:00Zoai:scielo:S0001-37652008000400002Revistahttp://www.scielo.br/aabchttps://old.scielo.br/oai/scielo-oai.php||aabc@abc.org.br1678-26900001-3765opendoar:2008-11-25T00:00Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)false
dc.title.none.fl_str_mv An elementary proof of MinVol(Rn) = 0 for n > 3
title An elementary proof of MinVol(Rn) = 0 for n > 3
spellingShingle An elementary proof of MinVol(Rn) = 0 for n > 3
Mei,Jiaqiang
minimal volume
smooth gluing
bounded geometry
title_short An elementary proof of MinVol(Rn) = 0 for n > 3
title_full An elementary proof of MinVol(Rn) = 0 for n > 3
title_fullStr An elementary proof of MinVol(Rn) = 0 for n > 3
title_full_unstemmed An elementary proof of MinVol(Rn) = 0 for n > 3
title_sort An elementary proof of MinVol(Rn) = 0 for n > 3
author Mei,Jiaqiang
author_facet Mei,Jiaqiang
Wang,Hongyu
Xu,Haifeng
author_role author
author2 Wang,Hongyu
Xu,Haifeng
author2_role author
author
dc.contributor.author.fl_str_mv Mei,Jiaqiang
Wang,Hongyu
Xu,Haifeng
dc.subject.por.fl_str_mv minimal volume
smooth gluing
bounded geometry
topic minimal volume
smooth gluing
bounded geometry
description In this paper, we give an elementary proof of the result that the minimal volumes of R³ and R4 are zero. The approach is to construct a sequence of explicit complete metrics on them such that the sectional curvatures are bounded in absolute value by 1 and the volumes tend to zero. As a direct consequence, we get that MinVol (Rn) = 0 for n > 3.
publishDate 2008
dc.date.none.fl_str_mv 2008-12-01
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=S0001-37652008000400002
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652008000400002
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0001-37652008000400002
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.80 n.4 2008
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
_version_ 1754302857197125632

Registros relacionados