Обобщение одной леммы Е. А. Полецкого на классы пространственных отображений

Севостьянов, Є. О. (2009) Обобщение одной леммы Е. А. Полецкого на классы пространственных отображений. Український математичний журнал, 61 (7). pp. 969-975. ISSN 1027-3190

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The paper is devoted to investigations in the field of space mappings. We prove that open discrete mappings f ∈ W1,n loc such that their outer dilatation KO(x, f) belongs to Ln−1 loc 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.

Item Type: Article
Subjects: Q Science > QA Mathematics > Mathematical Analysis
Divisions: Faculty of Physics and Mathematics > Department of Mathematical Analysis, Business Analysis and Statistics
Depositing User: Ірина Ігорівна Таргонська
Date Deposited: 10 Nov 2014 09:23
Last Modified: 08 Sep 2020 17:20
URI: http://eprints.zu.edu.ua/id/eprint/13845

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