Extremal decomposition of multidimensional complex space for five domains

The paper is devoted to one open extremal problem in the geometric function theory of complex variables associated with estimates of a functional defined on the systems of non-overlapping domains. We consider the problem of the maximum of a product of inner radii of n non-overlapping domains contain...

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Published in:Український математичний вісник
Date:2018
Main Authors: Zabolotni, i Y., Denega, I.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2018
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/169414
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Extremal decomposition of multidimensional complex space for five domains / Y. Zabolotnii, I. Denega // Український математичний вісник. — 2018. — Т. 15, № 3. — С. 431-441. — Бібліогр.: 21 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Zabolotni, i Y.
Denega, I.
author_facet Zabolotni, i Y.
Denega, I.
citation_txt Extremal decomposition of multidimensional complex space for five domains / Y. Zabolotnii, I. Denega // Український математичний вісник. — 2018. — Т. 15, № 3. — С. 431-441. — Бібліогр.: 21 назв. — англ.
collection DSpace DC
container_title Український математичний вісник
description The paper is devoted to one open extremal problem in the geometric function theory of complex variables associated with estimates of a functional defined on the systems of non-overlapping domains. We consider the problem of the maximum of a product of inner radii of n non-overlapping domains containing points of a unit circle and the power γ of the inner radius of a domain containing the origin. The problem was formulated in 1994 in Dubinin’s paper in the journal “Russian Mathematical Surveys” in the list of unsolved problems and then repeated in his monograph in 2014. Currently, it is not solved in general. In this paper, we obtained a solution of the problem for five simply connected domains and power γ ∈ (1, 2.57] and generalized this result to the case of multidimensional complex space.
first_indexed 2025-11-26T00:08:44Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1810-3200
language English
last_indexed 2025-11-26T00:08:44Z
publishDate 2018
publisher Інститут прикладної математики і механіки НАН України
record_format dspace
spelling Zabolotni, i Y.
Denega, I.
2020-06-12T17:53:31Z
2020-06-12T17:53:31Z
2018
Extremal decomposition of multidimensional complex space for five domains / Y. Zabolotnii, I. Denega // Український математичний вісник. — 2018. — Т. 15, № 3. — С. 431-441. — Бібліогр.: 21 назв. — англ.
1810-3200
010 MSC. 30C75, 32A30
https://nasplib.isofts.kiev.ua/handle/123456789/169414
The paper is devoted to one open extremal problem in the geometric function theory of complex variables associated with estimates of a functional defined on the systems of non-overlapping domains. We consider the problem of the maximum of a product of inner radii of n non-overlapping domains containing points of a unit circle and the power γ of the inner radius of a domain containing the origin. The problem was formulated in 1994 in Dubinin’s paper in the journal “Russian Mathematical Surveys” in the list of unsolved problems and then repeated in his monograph in 2014. Currently, it is not solved in general. In this paper, we obtained a solution of the problem for five simply connected domains and power γ ∈ (1, 2.57] and generalized this result to the case of multidimensional complex space.
en
Інститут прикладної математики і механіки НАН України
Український математичний вісник
Extremal decomposition of multidimensional complex space for five domains
Article
published earlier
spellingShingle Extremal decomposition of multidimensional complex space for five domains
Zabolotni, i Y.
Denega, I.
title Extremal decomposition of multidimensional complex space for five domains
title_full Extremal decomposition of multidimensional complex space for five domains
title_fullStr Extremal decomposition of multidimensional complex space for five domains
title_full_unstemmed Extremal decomposition of multidimensional complex space for five domains
title_short Extremal decomposition of multidimensional complex space for five domains
title_sort extremal decomposition of multidimensional complex space for five domains
url https://nasplib.isofts.kiev.ua/handle/123456789/169414
work_keys_str_mv AT zabolotniiy extremaldecompositionofmultidimensionalcomplexspaceforfivedomains
AT denegai extremaldecompositionofmultidimensionalcomplexspaceforfivedomains