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...
- 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
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
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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. |
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2017 |
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2017-01-01 |
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2019-07-03T02:07:29Z |
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2019-07-03T02:07:29Z |
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Artículo de revista |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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info:eu-repo/semantics/article |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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Text |
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http://purl.org/redcol/resource_type/ART |
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publishedVersion |
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ISSN: 2357-4100 |
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https://repositorio.unal.edu.co/handle/unal/66436 |
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http://bdigital.unal.edu.co/67464/ |
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ISSN: 2357-4100 |
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spa |
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spa |
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https://revistas.unal.edu.co/index.php/recolma/article/view/66832 |
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Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas Revista Colombiana de Matemáticas |
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Becker, Jochen and Pommerenke, Christian (2017) On analytic families of conformal maps. Revista Colombiana de Matemáticas, 51 (1). pp. 15-19. ISSN 2357-4100 |
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Derechos reservados - Universidad Nacional de Colombia |
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http://purl.org/coar/access_right/c_abf2 |
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Atribución-NoComercial 4.0 Internacional |
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info:eu-repo/semantics/openAccess |
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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 |
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