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This article is cited in 4 scientific papers (total 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.
Received April 17, 2018, published July 16, 2018
Citation:
V. V. Aseev, “On coordinate vector-functions of quasiregular mappings”, Sib. Èlektron. Mat. Izv., 15 (2018), 768–772
Linking options:
https://www.mathnet.ru/eng/semr950 https://www.mathnet.ru/eng/semr/v15/p768
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