Weakly quasisymmetric maps and uniform spaces

Yaxiang Li; Matti Vuorinen; Qingshan Zhou

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arXiv · 1705.05671

Weakly quasisymmetric maps and uniform spaces

Yaxiang Li·Matti Vuorinen·Qingshan Zhou

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Abstract

Suppose that $X$ and $Y$ are quasiconvex and complete metric spaces, that $G\subset X$ and $G'\subset Y$ are domains, and that $f: G\to G'$ is a homeomorphism. In this paper, we first give some basic properties of short arcs, and then we show that: if $f$ is a weakly quasisymmetric mapping and $G'$ is a quasiconvex domain, then the image $f(D)$ of every uniform subdomain $D$ in $G$ is uniform. As an application, we get that if $f$ is a weakly quasisymmetric mapping and $G'$ is an uniform domain, then the images of the short arcs in $G$ under $f$ are uniform arcs in the sense of diameter.

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BibTeX RIS

Yaxiang Li, Matti Vuorinen, Qingshan Zhou. 2017-05-15. Weakly quasisymmetric maps and uniform spaces. https://arxiv.org/abs/1705.05671

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