Generalization of one Poletskii lemma to classes of space mappings

  • E. A. Sevost’yanov

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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