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Conformal Modulus of the Exterior of Two Rectilinear Slits

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Abstract

We study moduli of planar ring domains whose complements are linear segments and establish formulas for their moduli in terms of the Weierstrass elliptic functions. Numerical tests are carried out to illustrate our results.

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Notes

  1. In contrast to [2], we denote by \(\omega _1\) and \(\omega _2\) periods of elliptic functions, not half-periods. The same remark concerns the values \(\eta _k\) defined by (2).

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Authors and Affiliations

  1. Kazan Federal University, 35, Kremlevskaya Str., Kazan, 420008, Russia

    D. Dautova & S. Nasyrov

  2. Department of Mathematics and Statistics, University of Turku, Turku, Finland

    M. Vuorinen

Authors
  1. D. Dautova
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  2. S. Nasyrov
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  3. M. Vuorinen
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Correspondence to S. Nasyrov.

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Communicated by Thomas Ransford.

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The work of the first author was supported by the Russian Foundation for Basic Research and the Government of the Republic of Tatarstan, Grant no. 18-41-160003; the second author was supported by the Russian Foundation for Basic Research, Grant no. 17-01-00282. The third author expresses his thanks to the Kazan Regional Scientific and Educational Mathematical Center for a support during his stay at Kazan Federal University FU in October–November 2018.

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Dautova, D., Nasyrov, S. & Vuorinen, M. Conformal Modulus of the Exterior of Two Rectilinear Slits. Comput. Methods Funct. Theory 21, 109–130 (2021). https://doi.org/10.1007/s40315-020-00315-y

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