This article is cited in 4 papers

Real, complex and functional analysis

On coordinate vector-functions of quasiregular mappings

V. V. Aseev

Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia

Abstract: Let $f:R^n \to R^n=R^k\times R^{n-k}$ ($1\leq k\leq n-1$) be a $K$-quasiregular mapping and $\pi: R^n\to R^k$ denotes the canonical projection. Then we obtain a lower estimate for the distortion of the values of generalized angles in $R^k$ under the multy-valued function $F=f^{-1}\circ \pi^{-1}: R^k \to R^n$. This estimate is Möbius invariant and depends only on $K$ and $n$.

Keywords: quasiregular map, conformal capacity of condenser, Teichmüller's ring, generalized angle, mapping of bounded angular distortion.

UDC: 517.54

MSC: 30C65

Received April 17, 2018, published July 16, 2018

Language: English

DOI: 10.17377/semi.2018.15.062

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