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On a Vӓisӓlӓ-type inequality for the angular dilatation of map**s and some of its applications

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Abstract

For a subtype of map**s with finite distortion f : D → D′, D, D′ ⊂ ℝn; n ≥ 2; which admit the existence of branch points, a modular inequality playing an essential role in the study of various problems of planar and spatial map**s is established. As an application, the problem of removal of isolated singularities of open discrete map**s with finite length distortion is investigated.

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Authors and Affiliations

  1. Institute of Mathematics of the NAS of Ukraine, Kiev, Ukraine

    Ruslan R. Salimov

  2. I. Franko Zhitomir State University, Zhitomir, Ukraine

    Evgeny A. Sevost’yanov

Authors
  1. Evgeny A. Sevost’yanov
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  2. Ruslan R. Salimov
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Corresponding author

Correspondence to Evgeny A. Sevost’yanov.

Additional information

Presented by V. Ya. Gutlyanskii

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 12, No. 4, pp. 511–538, September–December, 2015.

Translated from Russian by V. V. Kukhtin

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Sevost’yanov, E.A., Salimov, R.R. On a Vӓisӓlӓ-type inequality for the angular dilatation of map**s and some of its applications. J Math Sci 218, 69–88 (2016). https://doi.org/10.1007/s10958-016-3011-y

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  • DOI: https://doi.org/10.1007/s10958-016-3011-y

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