Estimates of products of some powers of inner radii for multiconnected domains
UDC 517.54 In this paper, we consider the problem of extreme partition of the complex plane, which is well-known in the geometric theory of functions. We obtain estimates of the maximum value for the product of some powers of inner radii of $n$ disjoint domains in the complex plane with respect to $...
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| Datum: | 2021 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2021
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/6682 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 517.54
In this paper, we consider the problem of extreme partition of the complex plane, which is well-known in the geometric theory of functions. We obtain estimates of the maximum value for the product of some powers of inner radii of $n$ disjoint domains in the complex plane with respect to $n$ arbitrary points of the plane. Estimates found in this paper can be applied to various problems of the geometric theory of functions. |
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| DOI: | 10.37863/umzh.v73i9.6682 |