Mean curvature flow of certain kind of isoparametric foliations on non-compact symmetric spaces

Abstract In this paper, we investigate the mean curvature flows starting from all leaves of theisoparametric foliation given by a certain kind of solvable group action on a symmetric space of non-compact type. We prove that the mean curvature flow starting from each non-minimal leaf of the foliation...

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Autor principal:	Koike,Naoyuki
Lenguaje:	English
Publicado:	Universidad de La Frontera. Departamento de Matemática y Estadística. 2018
Materias:	error function based activation function multivariate quasi-interpolation neural network approximation Kantorovich-Shilkret type operator
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462018000300013
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spelling	oai:scielo:S0719-064620180003000132019-03-08Mean curvature flow of certain kind of isoparametric foliations on non-compact symmetric spacesKoike,Naoyuki error function based activation function multivariate quasi-interpolation neural network approximation Kantorovich-Shilkret type operator Abstract In this paper, we investigate the mean curvature flows starting from all leaves of theisoparametric foliation given by a certain kind of solvable group action on a symmetric space of non-compact type. We prove that the mean curvature flow starting from each non-minimal leaf of the foliation exists in infinite time, if the foliation admits no minimal leaf, then the flow asymptotes the self-similar flow starting from another leaf, and if the foliation admits a minimal leaf (in this case, it is shown that there exists the only one minimal leaf), then the flow converges to the minimal leaf of the foliation in C∞-topology. These results give the geometric information between the leaves.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.20 n.3 20182018-10-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462018000300013en10.4067/S0719-06462018000300013
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	error function based activation function multivariate quasi-interpolation neural network approximation Kantorovich-Shilkret type operator
spellingShingle	error function based activation function multivariate quasi-interpolation neural network approximation Kantorovich-Shilkret type operator Koike,Naoyuki Mean curvature flow of certain kind of isoparametric foliations on non-compact symmetric spaces
description	Abstract In this paper, we investigate the mean curvature flows starting from all leaves of theisoparametric foliation given by a certain kind of solvable group action on a symmetric space of non-compact type. We prove that the mean curvature flow starting from each non-minimal leaf of the foliation exists in infinite time, if the foliation admits no minimal leaf, then the flow asymptotes the self-similar flow starting from another leaf, and if the foliation admits a minimal leaf (in this case, it is shown that there exists the only one minimal leaf), then the flow converges to the minimal leaf of the foliation in C∞-topology. These results give the geometric information between the leaves.
author	Koike,Naoyuki
author_facet	Koike,Naoyuki
author_sort	Koike,Naoyuki
title	Mean curvature flow of certain kind of isoparametric foliations on non-compact symmetric spaces
title_short	Mean curvature flow of certain kind of isoparametric foliations on non-compact symmetric spaces
title_full	Mean curvature flow of certain kind of isoparametric foliations on non-compact symmetric spaces
title_fullStr	Mean curvature flow of certain kind of isoparametric foliations on non-compact symmetric spaces
title_full_unstemmed	Mean curvature flow of certain kind of isoparametric foliations on non-compact symmetric spaces
title_sort	mean curvature flow of certain kind of isoparametric foliations on non-compact symmetric spaces
publisher	Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate	2018
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462018000300013
work_keys_str_mv	AT koikenaoyuki meancurvatureflowofcertainkindofisoparametricfoliationsonnoncompactsymmetricspaces
_version_	1714206800628154368

Mean curvature flow of certain kind of isoparametric foliations on non-compact symmetric spaces

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