Siberian Mathematical Journal

, Volume 51, Issue 5, pp 899–912

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

Article
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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 ⩽ 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.

Keywords

mapping with bounded distortion mapping with finite distortion modulus of a family of curves 

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© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Institute of Applied Mathematics and MechanicsDonetskUkraine

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