Uniformization of cofat domains on metric two-spheres

2025/04/19 by Li, Chengxi, Rajala, Kai · 1 citation
#30C20 #30C65 #30L10 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.14277

Abstract

We extend Schramm's cofat uniformization theorem to cofat domains on upper Ahlfors 2-regular metric two-spheres X. Specifically, we show that if Ω⊂ X is a cofat domain, then there exists a \fracπ2-quasiconformal homeomorphism f: Ω→ D onto a circle domain D ⊂ \mathbbS². Moreover, f preserves the point-components and non-trivial complementary components. We also construct examples which show that the above conclusions are not true for countably connected ℓ^α-subdomains of \mathbbS².

Citations

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Cited by

• Uniformization of metric surfaces: A survey

Related

• Quasisymmetric Koebe Uniformization
• Conformal Uniformization of Domains Bounded by Quasitripods
• Quasisymmetric Koebe Uniformization of metric surfaces
• Quasiconformal characterization of Schottky sets
• On the subinvariance of uniform domains in metric spaces