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An extremal problem for the maximum of product of the inner radii on a system of \(n+1\) mutually non-overlapping multiply connected domains \(D_k\) containing the points \(a_k\) , \(k = 1, \ldots , n\) , located on an arbitrary ellipse \(\frac {x^{2}}{d^{2}}+\frac {y^{2}}{t^{2}}=1\) , where \(d^{2}-t^{2}=1\) , and infinity is from the \(D_{n+1}\) is considered.

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Inequalities for the Inner Radii of Domains Containing an Arbitrary Ellipse Points and Infinity

  • 会议论文

  • 发表日期：

    2025年

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  • Iryna Denega,
  • Yaroslav Zabolotnyi

摘要

An extremal problem for the maximum of product of the inner radii on a system of \(n+1\) mutually non-overlapping multiply connected domains \(D_k\) containing the points \(a_k\) , \(k = 1, \ldots , n\) , located on an arbitrary ellipse \(\frac {x^{2}}{d^{2}}+\frac {y^{2}}{t^{2}}=1\) , where \(d^{2}-t^{2}=1\) , and infinity is from the \(D_{n+1}\) is considered.