The univalent Bloch-Landau constant, harmonic symmetry and conformal glueing

By modifying a domain first suggested by Ruth Goodman in 1935 and by exploiting the explicit solution by Fedorov of the Polyá-Chebotarev problem in the case of four symmetrically placed points, an improved upper bound for the univalent Bloch-Landau constant is obtained. The domain that leads to this...

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Detalles Bibliográficos
Autores: Carroll, Tom, Ortega Cerdà, Joaquim
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2009
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/43743
Acceso en línea:https://hdl.handle.net/2445/43743
Access Level:acceso abierto
Palabra clave:Teoria geomètrica de funcions
Funcions de variables complexes
Geometric function theory
Functions of complex variables
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spelling The univalent Bloch-Landau constant, harmonic symmetry and conformal glueingCarroll, TomOrtega Cerdà, JoaquimTeoria geomètrica de funcionsFuncions de variables complexesGeometric function theoryFunctions of complex variablesBy modifying a domain first suggested by Ruth Goodman in 1935 and by exploiting the explicit solution by Fedorov of the Polyá-Chebotarev problem in the case of four symmetrically placed points, an improved upper bound for the univalent Bloch-Landau constant is obtained. The domain that leads to this improved bound takes the form of a disk from which some arcs are removed in such a way that the resulting simply connected domain is harmonically symmetric in each arc with respect to the origin. The existence of domains of this type is established, using techniques from conformal welding, and some general properties of harmonically symmetric arcs in this setting are established.Elsevier Masson2009info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2445/43743Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésVersió postprint del document publicat a: http://dx.doi.org/10.1016/j.matpur.2009.05.008Journal de Mathématiques Pures et Appliquées, 2009, vol. 92, num. 4, p. 396-406http://dx.doi.org/10.1016/j.matpur.2009.05.008(c) Elsevier Masson, 2009info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/437432026-05-27T06:46:51Z
dc.title.none.fl_str_mv The univalent Bloch-Landau constant, harmonic symmetry and conformal glueing
title The univalent Bloch-Landau constant, harmonic symmetry and conformal glueing
spellingShingle The univalent Bloch-Landau constant, harmonic symmetry and conformal glueing
Carroll, Tom
Teoria geomètrica de funcions
Funcions de variables complexes
Geometric function theory
Functions of complex variables
title_short The univalent Bloch-Landau constant, harmonic symmetry and conformal glueing
title_full The univalent Bloch-Landau constant, harmonic symmetry and conformal glueing
title_fullStr The univalent Bloch-Landau constant, harmonic symmetry and conformal glueing
title_full_unstemmed The univalent Bloch-Landau constant, harmonic symmetry and conformal glueing
title_sort The univalent Bloch-Landau constant, harmonic symmetry and conformal glueing
dc.creator.none.fl_str_mv Carroll, Tom
Ortega Cerdà, Joaquim
author Carroll, Tom
author_facet Carroll, Tom
Ortega Cerdà, Joaquim
author_role author
author2 Ortega Cerdà, Joaquim
author2_role author
dc.subject.none.fl_str_mv Teoria geomètrica de funcions
Funcions de variables complexes
Geometric function theory
Functions of complex variables
topic Teoria geomètrica de funcions
Funcions de variables complexes
Geometric function theory
Functions of complex variables
description By modifying a domain first suggested by Ruth Goodman in 1935 and by exploiting the explicit solution by Fedorov of the Polyá-Chebotarev problem in the case of four symmetrically placed points, an improved upper bound for the univalent Bloch-Landau constant is obtained. The domain that leads to this improved bound takes the form of a disk from which some arcs are removed in such a way that the resulting simply connected domain is harmonically symmetric in each arc with respect to the origin. The existence of domains of this type is established, using techniques from conformal welding, and some general properties of harmonically symmetric arcs in this setting are established.
publishDate 2009
dc.date.none.fl_str_mv 2009
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/43743
url https://hdl.handle.net/2445/43743
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a: http://dx.doi.org/10.1016/j.matpur.2009.05.008
Journal de Mathématiques Pures et Appliquées, 2009, vol. 92, num. 4, p. 396-406
http://dx.doi.org/10.1016/j.matpur.2009.05.008
dc.rights.none.fl_str_mv (c) Elsevier Masson, 2009
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) Elsevier Masson, 2009
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier Masson
publisher.none.fl_str_mv Elsevier Masson
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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