Generalization of one Poletskii lemma to classes of space mappings

  • E. A. Sevost’yanov
Article

The paper is devoted to investigations in the field of space mappings. We prove that open discrete mappings fW1,nloc such that their outer dilatation KO(x, f) belongs to Ln−1loc and the measure of the set Bf of branching points of f is equal to zero have finite length distortion. In other words, the images of almost all curves γ in the domain D under the considered mappings f : D → ℝn, n ≥ 2, are locally rectifiable, f possesses the (N)-property with respect to length on γ, and, furthermore, the (N)-property also holds in the inverse direction for liftings of curves. The results obtained generalize the well-known Poletskii lemma proved for quasiregular mappings.

Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  • E. A. Sevost’yanov
    • 1
  1. 1.Institute of Applied Mathematics and MechanicsUkrainian National Academy of SciencesDonetskUkraine

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