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On lipschitz continuity of quasiconformalmappings in space

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Abstract

Sufficient conditions for a spatial quasiconformal mapping f to be Lipschitz or weak Lipschitz continuous at a prescribed point are given. The proofs of these results are based on new growth estimates for the conformal modulus under quasiconformal mappings f. The estimates are written in terms of integral means of the co-called pointwise angular dilatation coefficient.

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Authors and Affiliations

  1. Institute of Applied Mathematics And Mechanics, Nas of Ukraine, ul. Roze Luxemburg 74, 83114, Donetsk, Ukraine

    Vladimir Ya. Gutlyanskiĭ

  2. Department of Applied Mathematics, Holon Institute of Technology, 52 Golomb St., P.O.B. 305, 58102, Holon, Israel

    Anatoly Golberg

Authors
  1. Vladimir Ya. Gutlyanskiĭ
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  2. Anatoly Golberg
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Correspondence to Vladimir Ya. Gutlyanskiĭ.

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Gutlyanskiĭ, V.Y., Golberg, A. On lipschitz continuity of quasiconformalmappings in space. JAMA 109, 233–251 (2009). https://doi.org/10.1007/s11854-009-0032-1

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  • DOI: https://doi.org/10.1007/s11854-009-0032-1

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