Zolotarev's conformal mapping and Chebotarev's problem

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Consider the Chebotarev problem of finding a continuum S in the complex plane including some given points such that the logarithmic capacity of S is minimal. In this paper, we give a complete solution of this problem for the case of three given points with the help of Zolotarev's conformal mapping using Jacobian elliptic and theta functions. Moreover, for four given points, some special cases can be treated.

Original languageEnglish
Pages (from-to)118-133
Number of pages16
JournalIntegral Transforms and Special Functions
Issue number2
Publication statusPublished - 15 Feb 2015


  • Chebotarev's problem
  • Jacobian elliptic function
  • Jacobian theta function
  • logarithmiccapacity


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