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Quasiinvariance of the modulus of homotopic classes of curves and Teichmuller's problem

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Abstract

Results are obtained on the quasiconformal distortion of the modulus of one and several classes of punctiform curves on the plane. The relationship to Teichmuller's problem for a quadruple of points and the homotopic properties of extremal mappings are studied. In particular, the variation of the minimum deviations produced in different motions of one labeled point is studied.

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Literature cited

  1. J. Jenkins, Univalent Functions and Conformai Mappings [Russian translation], IL, Moscow (1962).

    Google Scholar 

  2. L. Alfors and L. Bers, Spaces of Riemannian Surfaces and Quasiconformal Mappings [Russian translation], IL, Moscow (1961).

    Google Scholar 

  3. S. L. Krushkal, Quasiconformal Mappings and Riemannian Surfaces [Russian translation], Nauka, Novosibirsk (1975).

    Google Scholar 

  4. G. V. Kuz'mina, “Moduli of families of curves and quadratic differentials,” Tr. Mat. Inst. Akad. Nauk SSSR,139, pp. 1–240 (1980).

    Google Scholar 

  5. P. M. Tamrazov, “Extremal metric method and conformal mappings,” Dissertation Abstract, Kiev (1963).

  6. E. G. Emel'yanov, “Certain properties of the moduli of families of curves,” Zap. Nauch. Sem. Leningr. Otd. Mat. Inst.,144, 72–82 (1985).

    Google Scholar 

  7. L. Alfors, Lectures on Quasiconformal Mappings [Russian translation], Mir, Moscow (1969).

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  8. O. Teichmuller, “Extremal quasiconformal mappings and quadratic differentials,” Abh. Preuss. Acad. Wiss., Math. Naturwiss., No. 22, pp. 3–197 (1940).

    Google Scholar 

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Authors and Affiliations

  1. Saratov Institute of Agricultural Mechanization, USSR

    A. Yu. Vasil'ev

Authors
  1. A. Yu. Vasil'ev
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 3, pp. 329–336, May–June, 1991.

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Vasil'ev, A.Y. Quasiinvariance of the modulus of homotopic classes of curves and Teichmuller's problem. Ukr Math J 43, 293–299 (1991). https://doi.org/10.1007/BF01060837

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  • DOI: https://doi.org/10.1007/BF01060837

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