Uniformization of cofat domains on metric two-spheres

IF 1.4 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2026-09-02 DOI:10.1112/jlms.70685

Chengxi Li, Kai Rajala

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引用次数: 0

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 $Ω \subset X$ is a cofat domain, then there exists a $\frac{π}{2}$ -quasiconformal homeomorphism $f : Ω \to D$ onto a circle domain $D \subset S^{2}$ . 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 $ℓ^{α}$ -subdomains of $S^{2}$ .

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度量二球上的色域均匀化

将Schramm的色均匀化定理推广到上Ahlfors 2正则度量双球X $X$上的色域。具体地说，我们证明了如果Ω∧X $\Omega \subset X$是一个重叠域，则存在π 2 $\frac{\pi }{2}$ -拟共形同胚f：Ω→D $f: \Omega \rightarrow D$到圆域D∧s2 $D \subset \mathbb {S}^2$。此外，f $f$保留了点分量和非平凡互补分量。我们还构造了一些例子，证明上述结论对于s2的可数连通的$\ell ^{\alpha }$ -子域$\mathbb {S}^2$是不成立的。

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.