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Some Unsolved Problems About Condenser Capacities on the Plane

  • Vladimir N. DubininEmail author
Chapter
Part of the Trends in Mathematics book series (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.

Keywords

Capacity of condenser Logarithmic capacity Relative capacity Symmetrization Asymptotic formulae Extremal decompositions 

2010 Mathematics Subject Classification

Primary: 31A15 31C15 31C20; Secondary: 30C85 30C70 

Notes

Acknowledgement

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

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Far Eastern Federal UniversityVladivostokRussia
  2. 2.Institute of Applied MathematicsVladivostokRussia

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