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Estimation of dilatations for mappings more general than quasiregular mappings

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We consider the so-called ring Q-mappings, which are natural generalizations of quasiregular mappings in a sense of Väisälä’s geometric definition of moduli. It is shown that, under the condition of nondegeneracy of these mappings, their inner dilatation is majorized by a function Q(x) to within a constant depending solely on the dimension of the space.

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Correspondence to R. R. Salimov.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 11, pp. 1531–1537, November, 2010.

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Salimov, R.R., Sevost’yanov, E.A. Estimation of dilatations for mappings more general than quasiregular mappings. Ukr Math J 62, 1775–1782 (2011). https://doi.org/10.1007/s11253-011-0467-2

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  • Quasiconformal Mapping
  • Maximum Elevation
  • Quasiregular Mapping
  • Lebesgue Measurable Function
  • Nonnegative Measurable Function