Quasiconformal homotopies of elementary space mappings. (Russian) Zbl 0701.30020

Abramov, I. V.; Roganov, E. A.

Mat. Sb. 180, No. 10, 1347-1354 (1989).

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