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On the openness and discreteness of mappings with unbounded characteristic of quasiconformality

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Ukrainian Mathematical Journal Aims and scope

The paper is devoted to the investigation of topological properties of space mappings. It is shown that orientation-preserving mappings \( f:D \to \overline {{\mathbb{R}^n}} \) in a domain \( D \subset {\mathbb{R}^n} \), n ≥ 2; which are more general than mappings with bounded distortion, are open and discrete if a function Q corresponding to the control of the distortion of families of curves under these mappings has slow growth in the domain f (D), e.g., if Q has finite mean oscillation at an arbitrary point y 0 ∈ f (D).

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Ukrainian National Academy of Sciences, Donetsk, Ukraine

    E. A. Sevost’yanov

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  1. E. A. Sevost’yanov
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 8, pp. 1128–1134, August, 2011.

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Sevost’yanov, E.A. On the openness and discreteness of mappings with unbounded characteristic of quasiconformality. Ukr Math J 63, 1298–1305 (2012). https://doi.org/10.1007/s11253-012-0578-4

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  • DOI: https://doi.org/10.1007/s11253-012-0578-4

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