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Quasiconformal homotopies of elementary space mappings. (Russian) Zbl 0701.30020
Let L: $$Q\to R^ n$$ be a non-degenerate mapping on a simplex Q and z an interior point of Q which decomposes Q into $$n+1$$ simplexes $$Q_ 0,Q_ 1,...,Q_ n$$. Denote by $${\mathcal F}=\{F\}$$ the class of all continuous mappings F: $$Q\to R^ n$$, which are affine on $$Q_ j$$ and coincide with L on the boundary of Q. It is proved in this paper that for very $$F\in {\mathcal F}$$, K[F]$$\geq K[L]$$ and the equality holds only if $$F=L$$. Every mapping F in $${\mathcal F}$$ allows a quasiconformal mapping homotopic to the identical mapping.
Reviewer: Li Zhong

##### MSC:
 30C99 Geometric function theory
##### Keywords:
quasiconformal mapping
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