On branch points of three-dimensional mappings with unbounded characteristic of quasiconformality - Sevost'yanov, E. A. (Ukrains’kyi Matematychnyi Zhurnal, 2011)
For the open discrete mappings f: D b → R3 of the domain D ⊂ R3 satisfying relatively general geometric conditions in D b and having the essential singularity b ∈ R3, 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 V ∩ f(Bf ) cannot be contained in the set A such that g(A) = I, where I = t ∈ R: |t| < 1 and g : U → Rn is a quasiconformal mapping of the domain U ⊂ Rn such that A ⊂ U.