Abstract
The aim of this note is to construct a ψ-uniform domain G in the complex plane C such that the identity mapping id: (G,jG)→(G,kG) is not an η-quasi-symmetric mapping for any homeomorphism η: [0,∞)→[0,∞). This result shows that the answer to the related open problem, posed by Hästö, Klén, Sahoo and Vuorinen, is negative.
| Original language | English |
|---|---|
| Pages (from-to) | 1114-1119 |
| Number of pages | 6 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 445 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Jan 2017 |
| MoE publication type | A1 Journal article-refereed |
Keywords
- Distance ratio metric
- Quasi-symmetric mapping
- Quasihyperbolic metric
- Uniform domain
- φ-uniform domain
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Wang, X., Zhou, Q., Guan, T., Huang, M., & Rasila, A. (2017). A note on the relationship between quasi-symmetric mappings and φ-uniform domains. Journal of Mathematical Analysis and Applications, 445(1), 1114-1119. https://doi.org/10.1016/j.jmaa.2016.07.049