On branch points of three-dimensional mappings with unbounded characteristic of quasiconformality

  • E. A. Sevost'yanov


For the open discrete mappings f: D \ {b} → R3 of the domain DR3 satisfying relatively general geometric conditions in D \ {b} and having the essential singularity bR3, we prove the following statement. Let y0 belong to R3 \ f (D \ {b}) and let the inner dilatation KI (x, f) and the outer dilatation KΟ (x, f) of the mapping f at a point x satisfy certain conditions. Denote by Bf the set of branch points of f. Then for an arbitrary neighborhood V of the point y0, a set Vf(Bf ) cannot be contained in the set A such that g(A) = I, where I = {tR: |t| < 1} and g : U Rn is a quasiconformal mapping of the domain U Rn such that AU.
How to Cite
Sevost’yanov, E. A. “On Branch Points of Three-Dimensional Mappings With Unbounded Characteristic of Quasiconformality”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, no. 1, Jan. 2011, pp. 69-79, https://umj.imath.kiev.ua/index.php/umj/article/view/2699.
Research articles