|
This article is cited in 1 scientific paper (total in 1 paper)
Quasiconformal homotopies of elementary space mappings
I. V. Abramov, E. A. Roganov
Abstract:
This article takes up the problem of a quasiconformal homotopy to the identity quasiconformal space mapping for the model case of an elementary piecewise-affine mapping of a simplex. In view here are continuous orientation-preserving mappings of the simplex that are affine on its boundary and in each simplex of the decomposition obtained by adding a single new vertex inside the original simplex. It is proved that an arbitrary elementary piecewise-affine mapping of the simplex admits a quasiconformal homotopy to the identity mapping.
The proof is based on the following assertion: the smallest coefficient of quasiconformality in the class of all elementary piecewise-affine mappings of the simplex that coincide on its boundary with some affine mapping belongs to this affine mapping. This result can be regarded as a multidimensional analogue of the classical Grötzsch problem on an extremal mapping of rectangles that deviates least from a conformal mapping.
Bibliography: 4 titles.
Received: 06.07.1988
Citation:
I. V. Abramov, E. A. Roganov, “Quasiconformal homotopies of elementary space mappings”, Mat. Sb., 180:10 (1989), 1347–1354; Math. USSR-Sb., 68:1 (1991), 205–212
Linking options:
https://www.mathnet.ru/eng/sm1664https://doi.org/10.1070/SM1991v068n01ABEH001372 https://www.mathnet.ru/eng/sm/v180/i10/p1347
|
Statistics & downloads: |
Abstract page: | 255 | Russian version PDF: | 78 | English version PDF: | 6 | References: | 50 | First page: | 1 |
|