On the sets of branch points of mappings more general than quasiregular
Abstract
It is shown that if a point x0∊ℝn,n≥3, is an essential isolated singularity of an open discrete Q-mapping f:D→¯ℝn,Bf is the set of branch points of f in D; and a point z0∊¯ℝn is an asymptotic limit of f at the point x0; then, for any neighborhood U containing the point x0; the point z0∊¯f(Bf∩U) provided that the function Q has either a finite mean oscillation at the point x0 or a logarithmic singularity whose order does not exceed n − 1: Moreover, for n ≥ 2; under the indicated conditions imposed on the function Q; every point of the set \overline{ℝ^n}\ f(D) is an asymptotic limit of f at the point x_0. For n ≥ 3, the following relation is true: \overline{ℝ^n}∖f(D) ⊂\overline{f(B_f ∩ U)}. In addition, if ∞ ∉ f(D), then the set f B_f is infinite and x_0 ∈ \overline{B_f}.Downloads
Published
25.02.2010
Issue
Section
Research articles
How to Cite
Sevost'yanov, E. A. “On the Sets of Branch Points of Mappings More General Than Quasiregular”. Ukrains’kyi Matematychnyi Zhurnal, vol. 62, no. 2, Feb. 2010, pp. 215–230, https://umj.imath.kiev.ua/index.php/umj/article/view/2858.