Article
| Title: | Lipschitz constants for a hyperbolic type metric under Möbius transformations (English) |
| Author: | Wu, Yinping |
| Author: | Wang, Gendi |
| Author: | Jia, Gaili |
| Author: | Zhang, Xiaohui |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 2 |
| Year: | 2024 |
| Pages: | 445-460 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $D$ be a nonempty open set in a metric space $(X,d)$ with $\partial D\neq \emptyset $. Define $$ h_{D,c}(x,y)=\log \bigg (1+c\frac {d(x,y)}{\sqrt {d_D(x)d_D(y)}}\bigg ), $$ where $d_D(x)=d(x,\partial D)$ is the distance from $x$ to the boundary of $D$. For every $c\geq 2$, $h_{D,c}$ is a metric. We study the sharp Lipschitz constants for the metric $h_{D,c}$ under Möbius transformations of the unit ball, the upper half space, and the punctured unit ball. (English) |
| Keyword: | Lipschitz constant |
| Keyword: | hyperbolic type metric |
| Keyword: | Möbius transformation |
| MSC: | 30C65 |
| MSC: | 51M10 |
| idZBL: | Zbl 07893393 |
| idMR: | MR4764534 |
| DOI: | 10.21136/CMJ.2024.0366-23 |
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| Date available: | 2024-07-10T14:53:03Z |
| Last updated: | 2024-12-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152452 |
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