This article is cited in 2 papers

Brief communications

Asymptotic curves and asymptotic values for mappings with weighted bounded $(p,q)$-distortion

M. V. Tryamkin

Chair of Higher Mathematics, Novosibirsk State University, 2 Pirogov str., Novosibirsk, 630090 Russia

Abstract: We prove that a mapping with weighted bounded $(p,q)$-distortion can be extended by continuity to a set whose family of asymptotic curves has modulus zero. We also establish a counterpart to Iversen's theorem for a mapping with weighted bounded $(n,n)$-distortion.

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

UDC: 517.547+517.518

Presented by the member of Editorial Board: S. K. Vodopyanov
Received: 31.07.2015

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:1, 76–80

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