Estimation of the maximum product of inner radii of mutually disjoint domains

  • O. K. Bakhtin Institute of Mathematics, National Academy of Sciences of Ukraine
  • I. V. Denega Institute of Mathematics, National Academy of Sciences of Ukraine, Kiev
Keywords: inner radius of domain, non-overlapping domains, the Green function, (n, m)-radial system of points, transfinite diameter, theorem on minimizing

Abstract

UDC 517.54

We establish effective upper estimates for the maximum products of the inner radii of mutually disjoint domains in the $(n,m)$-radial systems of points of the complex plane for all possible values of a certain  parameter $\gamma.$ We also obtain conditions under which the structure of points and domains is not important for our investigations. 

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Published
15.02.2020
How to Cite
BakhtinO. K., and DenegaI. V. “Estimation of the Maximum Product of Inner Radii of Mutually Disjoint Domains”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 2, Feb. 2020, pp. 173-8, http://umj.imath.kiev.ua/index.php/umj/article/view/1106.
Section
Research articles