On the sets of branch points of mappings more general than quasiregular

Authors

  • E. A. Sevost'yanov

Abstract

It is shown that if a point x0n,n3, is an essential isolated singularity of an open discrete Q-mapping f:D¯n,Bf is the set of branch points of f in D; and a point z0¯n is an asymptotic limit of f at the point x0; then, for any neighborhood U containing the point x0; the point z0¯f(BfU) 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}.

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.