Smooth approximation of Lipschitz functions on Finsler manifolds

We study the smooth approximation of Lipschitz functions on Finsler manifolds, keeping control on the corresponding Lipschitz constants. We prove that, given a Lipschitz function f : M -> R defined on a connected, second countable Finsler manifold M, for each positive continuous function epsilon...

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Detalles Bibliográficos
Autores: Garrido Carballo, María Isabel, Jaramillo Aguado, Jesús Ángel, Rangel, Yenny C.
Tipo de recurso: artículo
Fecha de publicación:2013
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/33358
Acceso en línea:https://hdl.handle.net/20.500.14352/33358
Access Level:acceso abierto
Palabra clave:514.7
Riemannian-manifolds
isometries
Geometría diferencial
1204.04 Geometría Diferencial
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oai_identifier_str oai:docta.ucm.es:20.500.14352/33358
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repository_id_str
spelling Smooth approximation of Lipschitz functions on Finsler manifoldsGarrido Carballo, María IsabelJaramillo Aguado, Jesús ÁngelRangel, Yenny C.514.7Riemannian-manifoldsisometriesGeometría diferencial1204.04 Geometría DiferencialWe study the smooth approximation of Lipschitz functions on Finsler manifolds, keeping control on the corresponding Lipschitz constants. We prove that, given a Lipschitz function f : M -> R defined on a connected, second countable Finsler manifold M, for each positive continuous function epsilon : M -> (0, infinity) and each r > 0, there exists a C-1-smooth Lipschitz function g : M -> R such that vertical bar f(x) - g(x)vertical bar <= epsilon(x), for every x is an element of M, and Lip(g) <= Lip(f) + r. As a consequence, we derive a completeness criterium in the class of what we call quasi-reversible Finsler manifolds. Finally, considering the normed algebra C-b(1)(M) of all C-1 functions with bounded derivative on a complete quasi-reversible Finsler manifold M, we obtain a characterization of algebra isomorphisms T : C-b(1)(N) -> C-b(1)(M) as composition operators. From this we obtain a variant of Myers-Nakai Theorem in the context of complete reversible Finsler manifolds.HindawiUniversidad Complutense de Madrid20132013-01-0120132013-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/33358reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/333582026-06-02T12:44:21Z
dc.title.none.fl_str_mv Smooth approximation of Lipschitz functions on Finsler manifolds
title Smooth approximation of Lipschitz functions on Finsler manifolds
spellingShingle Smooth approximation of Lipschitz functions on Finsler manifolds
Garrido Carballo, María Isabel
514.7
Riemannian-manifolds
isometries
Geometría diferencial
1204.04 Geometría Diferencial
title_short Smooth approximation of Lipschitz functions on Finsler manifolds
title_full Smooth approximation of Lipschitz functions on Finsler manifolds
title_fullStr Smooth approximation of Lipschitz functions on Finsler manifolds
title_full_unstemmed Smooth approximation of Lipschitz functions on Finsler manifolds
title_sort Smooth approximation of Lipschitz functions on Finsler manifolds
dc.creator.none.fl_str_mv Garrido Carballo, María Isabel
Jaramillo Aguado, Jesús Ángel
Rangel, Yenny C.
author Garrido Carballo, María Isabel
author_facet Garrido Carballo, María Isabel
Jaramillo Aguado, Jesús Ángel
Rangel, Yenny C.
author_role author
author2 Jaramillo Aguado, Jesús Ángel
Rangel, Yenny C.
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 514.7
Riemannian-manifolds
isometries
Geometría diferencial
1204.04 Geometría Diferencial
topic 514.7
Riemannian-manifolds
isometries
Geometría diferencial
1204.04 Geometría Diferencial
description We study the smooth approximation of Lipschitz functions on Finsler manifolds, keeping control on the corresponding Lipschitz constants. We prove that, given a Lipschitz function f : M -> R defined on a connected, second countable Finsler manifold M, for each positive continuous function epsilon : M -> (0, infinity) and each r > 0, there exists a C-1-smooth Lipschitz function g : M -> R such that vertical bar f(x) - g(x)vertical bar <= epsilon(x), for every x is an element of M, and Lip(g) <= Lip(f) + r. As a consequence, we derive a completeness criterium in the class of what we call quasi-reversible Finsler manifolds. Finally, considering the normed algebra C-b(1)(M) of all C-1 functions with bounded derivative on a complete quasi-reversible Finsler manifold M, we obtain a characterization of algebra isomorphisms T : C-b(1)(N) -> C-b(1)(M) as composition operators. From this we obtain a variant of Myers-Nakai Theorem in the context of complete reversible Finsler manifolds.
publishDate 2013
dc.date.none.fl_str_mv 2013
2013-01-01
2013
2013-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/33358
url https://hdl.handle.net/20.500.14352/33358
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Hindawi
publisher.none.fl_str_mv Hindawi
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.198674

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