This article is cited in 2 papers

Real, complex and functional analysis

On asymptotic curves and values in the theory of mappings with weighted bounded distortion

M. V. Tryamkin

Novosibirsk State University, Pirogova st. 2, 630090, Novosibirsk, Russia

Abstract: We show that a mapping with weighted bounded $(p,q)$-distortion can be extended to the set whose family of asymptotic curves has weighted modulus zero. We also state some results about asymptotic values, in particular, the counterpart to Iversen's theorem for mappings with weighted bounded $(n,n)$-distortion.

Keywords: mapping with weighted bounded $(p,q)$-distortion, asymptotic curve, asymptotic value, singularity, capacity, modulus.

UDC: 517.54

MSC: 30C65

Received August 15, 2015, published September 28, 2015

Language: English

DOI: 10.17377/semi.2015.12.054