On the stability of $\phi$-uniform domains
| Autor: | Klén, R., Li, Y., Sahoo, S. K., Vuorinen, M. |
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| Rok vydání: | 2008 |
| Předmět: | |
| Zdroj: | Monatshefte f\"ur Mathematik, 174 (2)(2014), 231 - 258 |
| Druh dokumentu: | Working Paper |
| Popis: | We study two metrics, the quasihyperbolic metric and the distance ratio metric of a subdomain $G \subset {\mathbb R}^n$. In the sequel, we investigate a class of domains, so called $\varphi$-uniform domains, defined by the property that these two metrics are comparable with respect to a homeomorphism $\varphi$ from $[0,\infty)$ to itself. Finally, we discuss a number of stability properties of $\varphi$-uniform domains. In particular, we show that the class of $\varphi$-uniform domains is stable in the sense that removal of a geometric sequence of points from a $\varphi$-uniform domain yields a $\varphi_1$-uniform domain. Comment: 23 pages, 7 figures |
| Databáze: | arXiv |
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