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On Distortions of the Transfinite Diameter of Disk Image

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Ukrainian Mathematical Journal Aims and scope

We study the so-called ring Q-homeomorphisms with respect to the p-modulus for p > 2 in the complex plane. In particular, we establish a lower bound for the distortion of the transfinite diameter of disk image. Moreover, we solve the problem of minimization of the functional of distortion of the transfinite diameter of a disk in a certain class of ring Q-homeomorphisms with respect to the p-modulus.

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    R. Salimov, L. Vyhivska & B. Klishchuk

  2. Wrocław University of Science and Technology, Wrocław, Poland

    L. Vyhivska

Authors
  1. R. Salimov
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  2. L. Vyhivska
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  3. B. Klishchuk
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Correspondence to B. Klishchuk.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, No. 2, pp. 207–214, February, 2023. Ukrainian DOI: https://doi.org/10.37863/umzh.v75i2.7329.

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Salimov, R., Vyhivska, L. & Klishchuk, B. On Distortions of the Transfinite Diameter of Disk Image. Ukr Math J 75, 235–243 (2023). https://doi.org/10.1007/s11253-023-02196-5

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  • DOI: https://doi.org/10.1007/s11253-023-02196-5

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