On the stability of $��$-uniform domains
| Autor: | Kl��n, R., Li, Y., Sahoo, S. K., Vuorinen, M. |
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| Rok vydání: | 2008 |
| Předmět: | |
| DOI: | 10.48550/arxiv.0812.4369 |
| 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 $��$-uniform domains, defined by the property that these two metrics are comparable with respect to a homeomorphism $��$ from $[0,\infty)$ to itself. Finally, we discuss a number of stability properties of $��$-uniform domains. In particular, we show that the class of $��$-uniform domains is stable in the sense that removal of a geometric sequence of points from a $��$-uniform domain yields a $��_1$-uniform domain. 23 pages, 7 figures |
| Databáze: | OpenAIRE |
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