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Some Unsolved Problems About Condenser Capacities on the Plane

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Complex Analysis and Dynamical Systems

Part of the book series: Trends in Mathematics ((TM))

Abstract

In the paper we pose fourteen open problems of Potential Theory involved the conformal capacity of condensers with three and more plates, the logarithmic capacity, the relative capacity and extremal decompositions of the unit disk or the Riemann sphere. All problems are closely related to various applications in Geometric Function Theory of a complex variable.

Dedicated to the memory of my friend Sasha Vasil’ev

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Acknowledgement

Vladimir N. Dubinin was supported by the Russian Science Foundation (Grant 14-11-00022).

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Authors and Affiliations

  1. Far Eastern Federal University, Vladivostok, Russia

    Vladimir N. Dubinin

  2. Institute of Applied Mathematics, Vladivostok, Russia

    Vladimir N. Dubinin

Authors
  1. Vladimir N. Dubinin
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Correspondence to Vladimir N. Dubinin .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel

    Mark Agranovsky

  2. Department of Mathematics, Holon Institute of Technology, Holon, Israel

    Anatoly Golberg

  3. Department of Mathematics, ORT Braude College, Karmiel, Israel

    Fiana Jacobzon

  4. Department of Mathematics, Holon Institute of Technology, Holon, Israel

    David Shoikhet

  5. Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel

    Lawrence Zalcman

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Dubinin, V.N. (2018). Some Unsolved Problems About Condenser Capacities on the Plane. In: Agranovsky, M., Golberg, A., Jacobzon, F., Shoikhet, D., Zalcman, L. (eds) Complex Analysis and Dynamical Systems. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-70154-7_5

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