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Extremal decomposition of a multidimensional complex space for five domains
- Source :
- Journal of Mathematical Sciences. 241:101-108
- Publication Year :
- 2019
- Publisher :
- Springer Science and Business Media LLC, 2019.
-
Abstract
- 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.
- Subjects :
- Statistics and Probability
Pure mathematics
Geometric function theory
Applied Mathematics
General Mathematics
010102 general mathematics
01 natural sciences
010305 fluids & plasmas
symbols.namesake
Unit circle
Complex space
Product (mathematics)
Green's function
0103 physical sciences
Simply connected space
Decomposition (computer science)
symbols
0101 mathematics
Quadratic differential
Mathematics
Subjects
Details
- ISSN :
- 15738795 and 10723374
- Volume :
- 241
- Database :
- OpenAIRE
- Journal :
- Journal of Mathematical Sciences
- Accession number :
- edsair.doi...........d2e052049c666853e5955fba00d13d21