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...
Gespeichert in:
| Veröffentlicht in: | Український математичний вісник |
|---|---|
| Datum: | 2018 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2018
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/169414 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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.
|
|---|---|
| ISSN: | 1810-3200 |