On analytic families of conformal maps

Let Λ be a domain in C and let fλ(z) = z + a0(λ) + a1(λ)z −1 + ... be meromorphic in D∗ := {z ∈ C : |z| 1} ∪ {∞}. We assume that fλ(z) is holomorphic in λ ∈ Λ for fixed z.The main theorem states: Let Λ0 be a subdomain of Λ such that fλ is univalent in D∗ for λ ∈ Λ0. If fλ0 has a quasiconformal exten...

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Autores:
Becker, Jochen
Pommerenke, Christian
Tipo de recurso:
Article of journal
Fecha de publicación:
2017
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/66436
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/66436
http://bdigital.unal.edu.co/67464/
Palabra clave:
51 Matemáticas / Mathematics
Funciones univalentes
extensión cuasiconforme
parámetro analítico
desigualdad de Grunsky
Univalent function
quasiconformal extension
analytic parameter
Grunsky inequality
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openAccess
License
Atribución-NoComercial 4.0 Internacional
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spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Becker, Jochenabb75796-39b6-499d-9b22-472c3cb0e5b0300Pommerenke, Christian4999ea34-cb26-4530-bec3-81efd88b32c53002019-07-03T02:07:29Z2019-07-03T02:07:29Z2017-01-01ISSN: 2357-4100https://repositorio.unal.edu.co/handle/unal/66436http://bdigital.unal.edu.co/67464/Let Λ be a domain in C and let fλ(z) = z + a0(λ) + a1(λ)z −1 + ... be meromorphic in D∗ := {z ∈ C : |z| 1} ∪ {∞}. We assume that fλ(z) is holomorphic in λ ∈ Λ for fixed z.The main theorem states: Let Λ0 be a subdomain of Λ such that fλ is univalent in D∗ for λ ∈ Λ0. If fλ0 has a quasiconformal extension to the closure of D∗ for one λ0 ∈ Λ0 then fλ has a quasiconformal extension for all λ ∈ Λ0.This result is related to a theorem of Mañé, Sad and Sullivan (1983) where the assumptions are however different. The main tool of our proof is the Grunsky inequality for univalent functions.Sea Λ a dominio en C y sea fλ(z) = z + a0(λ) + a1(λ)z −1 + ... meromorfa en D∗ := {z ∈ C : |z| 1} ∪ {∞}. Suponemos que fλ(z) es holomorfa en λ ∈ Λ para z fijo.El teorema principal dice: Sea Λ0 un subdominio de Λ tal que fλ es univalente en D∗ para λ ∈ Λ0. Si fλ0 tiene una extensión cuasiconforme a la clausura de D∗ para un λ0 ∈ Λ0 entonces fλ tiene una extensión cuasiconforme para todo λ ∈ Λ0.Este resultado está relacionado a un teorema de Mañé, Sad y Sullivan (1983) donde sin embargo las hipótesis son diferentes. Para nuestra demostración la herramienta principal es la desigualdad de Grunsky para funciones univalentes.application/pdfspaUniversidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticas - Sociedad Colombiana de Matemáticashttps://revistas.unal.edu.co/index.php/recolma/article/view/66832Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de MatemáticasRevista Colombiana de MatemáticasBecker, Jochen and Pommerenke, Christian (2017) On analytic families of conformal maps. Revista Colombiana de Matemáticas, 51 (1). pp. 15-19. ISSN 2357-410051 Matemáticas / MathematicsFunciones univalentesextensión cuasiconformeparámetro analíticodesigualdad de GrunskyUnivalent functionquasiconformal extensionanalytic parameterGrunsky inequalityOn analytic families of conformal mapsArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTORIGINAL66832-342834-1-SM.pdfapplication/pdf360899https://repositorio.unal.edu.co/bitstream/unal/66436/1/66832-342834-1-SM.pdf8f70083384189727835e92f586c29fd3MD51THUMBNAIL66832-342834-1-SM.pdf.jpg66832-342834-1-SM.pdf.jpgGenerated Thumbnailimage/jpeg4925https://repositorio.unal.edu.co/bitstream/unal/66436/2/66832-342834-1-SM.pdf.jpg482a193ee74595f5b7d2bee21757c9ebMD52unal/66436oai:repositorio.unal.edu.co:unal/664362023-05-25 23:02:42.564Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv On analytic families of conformal maps
title On analytic families of conformal maps
spellingShingle On analytic families of conformal maps
51 Matemáticas / Mathematics
Funciones univalentes
extensión cuasiconforme
parámetro analítico
desigualdad de Grunsky
Univalent function
quasiconformal extension
analytic parameter
Grunsky inequality
title_short On analytic families of conformal maps
title_full On analytic families of conformal maps
title_fullStr On analytic families of conformal maps
title_full_unstemmed On analytic families of conformal maps
title_sort On analytic families of conformal maps
dc.creator.fl_str_mv Becker, Jochen
Pommerenke, Christian
dc.contributor.author.spa.fl_str_mv Becker, Jochen
Pommerenke, Christian
dc.subject.ddc.spa.fl_str_mv 51 Matemáticas / Mathematics
topic 51 Matemáticas / Mathematics
Funciones univalentes
extensión cuasiconforme
parámetro analítico
desigualdad de Grunsky
Univalent function
quasiconformal extension
analytic parameter
Grunsky inequality
dc.subject.proposal.spa.fl_str_mv Funciones univalentes
extensión cuasiconforme
parámetro analítico
desigualdad de Grunsky
Univalent function
quasiconformal extension
analytic parameter
Grunsky inequality
description Let Λ be a domain in C and let fλ(z) = z + a0(λ) + a1(λ)z −1 + ... be meromorphic in D∗ := {z ∈ C : |z| 1} ∪ {∞}. We assume that fλ(z) is holomorphic in λ ∈ Λ for fixed z.The main theorem states: Let Λ0 be a subdomain of Λ such that fλ is univalent in D∗ for λ ∈ Λ0. If fλ0 has a quasiconformal extension to the closure of D∗ for one λ0 ∈ Λ0 then fλ has a quasiconformal extension for all λ ∈ Λ0.This result is related to a theorem of Mañé, Sad and Sullivan (1983) where the assumptions are however different. The main tool of our proof is the Grunsky inequality for univalent functions.
publishDate 2017
dc.date.issued.spa.fl_str_mv 2017-01-01
dc.date.accessioned.spa.fl_str_mv 2019-07-03T02:07:29Z
dc.date.available.spa.fl_str_mv 2019-07-03T02:07:29Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.identifier.issn.spa.fl_str_mv ISSN: 2357-4100
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/66436
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/67464/
identifier_str_mv ISSN: 2357-4100
url https://repositorio.unal.edu.co/handle/unal/66436
http://bdigital.unal.edu.co/67464/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.spa.fl_str_mv https://revistas.unal.edu.co/index.php/recolma/article/view/66832
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas
Revista Colombiana de Matemáticas
dc.relation.references.spa.fl_str_mv Becker, Jochen and Pommerenke, Christian (2017) On analytic families of conformal maps. Revista Colombiana de Matemáticas, 51 (1). pp. 15-19. ISSN 2357-4100
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Universidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticas - Sociedad Colombiana de Matemáticas
institution Universidad Nacional de Colombia
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