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Journal of Mathematical Sciences

, Volume 242, Issue 6, pp 787–795 | Cite as

Estimates of the inner radii of non-overlapping domains

  • Iryna DenegaEmail author
Article
  • 11 Downloads

Abstract

Some extremal problems of the geometric theory of functions of a complex variable related to the estimates of functionals defined on systems of non-overlapping domains are considered. Till now, many such problems have not been solved, though some partial solutions are available. In the paper, the improved method is proposed for solving the problems on extremal decomposition of the complex plane. The main results generalize and strengthen some known results in the theory of non-overlapping domains with free poles to the case of an arbitrary arrangement of systems of points on the complex plane.

Keywords

Inner radius of a domain non-overlapping domains Green’s function transfinite diameter theorem on minimizing of the area Cauchy inequality 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Mathematics of the National Academy of Sciences of UkraineKievUkraine

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