Estimates of the products of inner radii for multiconnected domains
УДК 517.54 We consider the known problem of geometric function theory on extremal partition of the complex plane. For this problem, we obtain estimates for the maximum value of the product of inner radii of $n$ disjoint domains with respect to $n$ arbitrary points in the complex plane. The exact sol...
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| Date: | 2021 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2021
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/6200 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | УДК 517.54
We consider the known problem of geometric function theory on extremal partition of the complex plane. For this problem, we obtain estimates for the maximum value of the product of inner radii of $n$ disjoint domains with respect to $n$ arbitrary points in the complex plane. The exact solutions to this problem are currently known only for $n = 2,3,4.$ In this paper, we found estimates that can be applied to various extremal geometric problems of the theory of functions. |
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| DOI: | 10.37863/umzh.v73i1.6200 |