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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Format: | Article |
Language: | English |
Published: |
De Gruyter
2021-11-01
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Series: | Analysis and Geometry in Metric Spaces |
Subjects: | |
Online Access: | https://doi.org/10.1515/agms-2020-0127 |
Summary: | 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. |
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ISSN: | 2299-3274 |