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 followingstatement. Let y0 belong to R3 \ f (D \ {b}) and let the inner dilatation KI (x, f) and the outer dilatationKΟ (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 theset 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.