Quasiconformal Jordan Domains

Quasiconformal Jordan Domains

We extend the classical Carathéodory extension theorem to quasiconformal Jordan domains (Y, dY). We say that a metric space (Y, dY) is a quasiconformal Jordan domain if the completion ̄Y of (Y, dY) has finite Hausdorff 2-measure, the boundary ∂Y = ̄Y \ Y is homeomorphic to 𝕊1, and there exists a hom...

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Autor principal: Ikonen Toni
Formato: article
Lenguaje:EN
Publicado: De Gruyter 2021
Materias:
quasiconformal
metric surface
carathéodory
beurling–ahlfors
primary 30l10
secondary 30c65, 28a75, 51f99
Analysis
QA299.6-433
Acceso en línea:https://doaj.org/article/b3cdbb65a0f94081bf8daedd49e15a4c
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spelling oai:doaj.org-article:b3cdbb65a0f94081bf8daedd49e15a4c2021-12-05T14:10:38ZQuasiconformal Jordan Domains2299-327410.1515/agms-2020-0127https://doaj.org/article/b3cdbb65a0f94081bf8daedd49e15a4c2021-11-01T00:00:00Zhttps://doi.org/10.1515/agms-2020-0127https://doaj.org/toc/2299-3274We extend the classical Carathéodory extension theorem to quasiconformal Jordan domains (Y, dY). We say that a metric space (Y, dY) is a quasiconformal Jordan domain if the completion ̄Y of (Y, dY) has finite Hausdorff 2-measure, the boundary ∂Y = ̄Y \ Y is homeomorphic to 𝕊1, and there exists a homeomorphism ϕ: 𝔻 →(Y, dY) that is quasiconformal in the geometric sense.Ikonen ToniDe Gruyterarticlequasiconformalmetric surfacecarathéodorybeurling–ahlforsprimary 30l10secondary 30c65, 28a75, 51f99AnalysisQA299.6-433ENAnalysis and Geometry in Metric Spaces, Vol 9, Iss 1, Pp 167-185 (2021)
institution DOAJ
collection DOAJ
language EN
topic quasiconformal
metric surface
carathéodory
beurling–ahlfors
primary 30l10
secondary 30c65, 28a75, 51f99
Analysis
QA299.6-433
spellingShingle quasiconformal
metric surface
carathéodory
beurling–ahlfors
primary 30l10
secondary 30c65, 28a75, 51f99
Analysis
QA299.6-433
Ikonen Toni
Quasiconformal Jordan Domains
description We extend the classical Carathéodory extension theorem to quasiconformal Jordan domains (Y, dY). We say that a metric space (Y, dY) is a quasiconformal Jordan domain if the completion ̄Y of (Y, dY) has finite Hausdorff 2-measure, the boundary ∂Y = ̄Y \ Y is homeomorphic to 𝕊1, and there exists a homeomorphism ϕ: 𝔻 →(Y, dY) that is quasiconformal in the geometric sense.
format article
author Ikonen Toni
author_facet Ikonen Toni
author_sort Ikonen Toni
title Quasiconformal Jordan Domains
title_short Quasiconformal Jordan Domains
title_full Quasiconformal Jordan Domains
title_fullStr Quasiconformal Jordan Domains
title_full_unstemmed Quasiconformal Jordan Domains
title_sort quasiconformal jordan domains
publisher De Gruyter
publishDate 2021
url https://doaj.org/article/b3cdbb65a0f94081bf8daedd49e15a4c
work_keys_str_mv AT ikonentoni quasiconformaljordandomains
_version_ 1718371860747386880

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