On the Branch Points of Mappings with the Unbounded Coefficient of Quasiconformality

We study relations between the quantity characterizing the distortion of families of curves under a given mapping and the structure of the branch point set of this mapping. For n ⩽ 3 we establish that the image of the branch point set of an open discrete mapping with an isolated essential singularity is an unbounded set in Rⁿ provided that the mapping satisfies certain geometric conditions controlling the distortion of concentric annuli centered at this point.