Zolotarev's conformal mapping and Chebotarev's problem

Research output: Contribution to journalArticlepeer-review

Abstract

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
Volume26
Issue number2
DOIs
Publication statusPublished - 15 Feb 2015

Keywords

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

Fingerprint Dive into the research topics of 'Zolotarev's conformal mapping and Chebotarev's problem'. Together they form a unique fingerprint.

Cite this