Generalization of one Poletskii lemma to classes of space mappings |
| |
Authors: | E A Sevost’yanov |
| |
Institution: | 1.Institute of Applied Mathematics and Mechanics,Ukrainian National Academy of Sciences,Donetsk,Ukraine |
| |
Abstract: | The paper is devoted to investigations in the field of space mappings. We prove that open discrete mappings f ∈ W
1,n
loc such that their outer dilatation K
O
(x, f) belongs to L
n−1
loc and the measure of the set B
f
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 → ℝ
n
, 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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|