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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb., 2017 Volume 208, Number 3, Pages 72–95 (Mi sm8645)

This article is cited in 3 papers

Some observations concerning multidimensional quasiconformal mappings

V. A. Zorich

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: For several important objects and quantities in the theory of quasiconformal space mappings, we discuss their dependence on the dimension of the space. In particular, in connection with the global homeomorphism theorem and the theorem on the injectivity radius of quasiconformal immersions, we consider the asymptotic behaviour of the moduli of Grötzsch and Teichmüller rings with respect to the dimension.
Bibliography: 23 titles.

Keywords: quasiconformal mapping, injectivity radius, conformal capacity, Grötzsch ring, Teichmüller ring.

UDC: 517.54+514.774

MSC: Primary 30C65; Secondary 30C62, 53D10

Received: 07.12.2015 and 04.04.2016

DOI: 10.4213/sm8645


 English version:
Sbornik: Mathematics, 2017, 208:3, 377–398

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