Uniformization of cofat domains on metric two-spheres
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915251402833920 |
|---|---|
| author | Li, Chengxi Rajala, Kai |
| author_facet | Li, Chengxi Rajala, Kai |
| contents | We extend \emph{Schramm's cofat uniformization theorem} to cofat domains on upper Ahlfors 2-regular metric two-spheres $X$. Specifically, we show that if $Ω\subset X$ is a cofat domain, then there exists a $\fracπ{2}$-quasiconformal homeomorphism $f: Ω\to D$ onto a circle domain $D \subset \mathbb{S}^2$. 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 $\ell^α$-subdomains of $\mathbb{S}^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14277 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniformization of cofat domains on metric two-spheres Li, Chengxi Rajala, Kai Complex Variables 30L10, 30C65, 30C20 We extend \emph{Schramm's cofat uniformization theorem} to cofat domains on upper Ahlfors 2-regular metric two-spheres $X$. Specifically, we show that if $Ω\subset X$ is a cofat domain, then there exists a $\fracπ{2}$-quasiconformal homeomorphism $f: Ω\to D$ onto a circle domain $D \subset \mathbb{S}^2$. 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 $\ell^α$-subdomains of $\mathbb{S}^2$. |
| title | Uniformization of cofat domains on metric two-spheres |
| topic | Complex Variables 30L10, 30C65, 30C20 |
| url | https://arxiv.org/abs/2504.14277 |