Quasiconformal Jordan Domains

Abstract

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.

Keywords

• quasiconformal
• metric surface
• carathéodory
• beurling–ahlfors
• primary 30l10
• secondary 30c65, 28a75, 51f99