An Extremal Problem on Non-overlapping Domains Containing Ellipse Points

Yaroslav Zabolotnii; Iryna Denega

doi:10.32523/2077-9879-2021-12-4-82-91

An Extremal Problem on Non-overlapping Domains Containing Ellipse Points

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Authors

Yaroslav Zabolotnii
Iryna Denega

DOI:

https://doi.org/10.32523/2077-9879-2021-12-4-82-91

Keywords:

inner radius of the domain, mutually non-overlapping domains, Green function, quadratic differential, Goluzin theorem

Abstract

An extremal problem of geometric function theory of a complex variable for the maximum of products of the inner radii on a system of n mutually non-overlapping multiply connected domains Bk containing the points ak, k = 1, n, located on an arbitrary ellipse x²/d² + y²/t² = 1 for which d²−t² = 1, is solved.

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Published

2021-12-30

How to Cite

Zabolotnii, Y., & Denega, I. (2021). An Extremal Problem on Non-overlapping Domains Containing Ellipse Points. Eurasian Mathematical Journal, 12(4), 82–91. https://doi.org/10.32523/2077-9879-2021-12-4-82-91