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The Vuorinen problem on the maximum of the conformal module

A problem on the maximum of the conformal module in a family of doubly connected domains in the unit disk, which is a hyperbolic analog of the Teichmüller problem, is solved. The cases where the maximum in question is expressed in terms of elliptic functions are established. Bibliography: 6 titles.


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Correspondence to E. G. Emel’yanov.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 404, 2012, pp. 120–134.

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Emel’yanov, E.G., Kuz’mina, G.V. The Vuorinen problem on the maximum of the conformal module. J Math Sci 193, 66–74 (2013).

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  • Unit Disk
  • Elliptic Function
  • Conformal Module
  • Hyperbolic Analog