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About one extremal problem for open sets and partially non-overlapping domains

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Abstract

Sharp estimates of a product of the inner radii for pairwise disjoint domains are obtained. In particular, we solve an extremal problem in the case of any finite number of free poles on the rays.

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Author information

Correspondence to Andrey L. Targonskii.

Additional information

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 16, No. 2, pp. 228–238 April–June, 2019.

The authors are grateful to Prof. A. K. Bakhtin for suggesting the problem and useful discussions.

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Targonskii, A.L., Targonskaya, I.I. & Vaschenko, K. About one extremal problem for open sets and partially non-overlapping domains. J Math Sci 244, 56–64 (2020) doi:10.1007/s10958-019-04604-3

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Keywords

  • Inner radius of a domain
  • quadratic differential
  • piecewise separating transformation
  • Green function
  • radial systems of points
  • logarithmic capacity
  • variational formula