Abstract:
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 $n\ge3$ 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 $\mathbb R^n$ provided that the mapping satisfies certain geometric conditions controlling the distortion of concentric annuli centered at this point.
Keywords:mapping with bounded distortion, mapping with finite distortion, modulus of a family of curves.
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