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Mat. Sb., 2017, Volume 208, Number 3, Pages 72–95 (Mi msb8645)  

This article is cited in 2 scientific papers (total 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.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00709-а
13-01-12417-офи-м
17-01-00592-а
This research was carried out with the support of the Russian Foundation for Basic Research (grant nos. 14-01-00709_a and 17-01-00592_а).


DOI: https://doi.org/10.4213/sm8645

Full text: PDF file (926 kB)
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English version:
Sbornik: Mathematics, 2017, 208:3, 377–398

Bibliographic databases:

UDC: 517.54+514.774
MSC: Primary 30C65; Secondary 30C62, 53D10
Received: 07.12.2015 and 04.04.2016

Citation: V. A. Zorich, “Some observations concerning multidimensional quasiconformal mappings”, Mat. Sb., 208:3 (2017), 72–95; Sb. Math., 208:3 (2017), 377–398

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/msb/v208/i3/p72

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. A. Zorich, “On the Isotopy Problem for Quasiconformal Mappings”, Proc. Steklov Inst. Math., 298 (2017), 129–132  mathnet  crossref  crossref  isi  elib
    2. A. I. Aptekarev, V. M. Buchstaber, V. A. Vassiliev, M. L. Gromov, Yu. S. Ilyashenko, B. S. Kashin, V. M. Keselman, V. V. Kozlov, M. L. Kontsevich, I. M. Krichever, N. G. Kruzhilin, S. K. Lando, Yu. I. Manin, G. A. Margulis, S. Yu. Nemirovski, S. P. Novikov, Yu. G. Reshetnyak, Ya. G. Sinai, S. P. Suetin, D. V. Treschev, D. B. Fuchs, A. G. Khovanskii, E. M. Chirka, A. S. Schwarz, A. N. Shiryaev, “Vladimir Antonovich Zorich (on his 80th birthday)”, Russian Math. Surveys, 73:5 (2018), 935–939  mathnet  crossref  crossref  adsnasa  isi  elib
    3. B. N. Apanasov, “Topological barriers for locally homeomorphic quasiregular mappings in 3-space”, Ann. Acad. Sci. Fenn. Math., 43:2 (2018), 579–596  crossref  mathscinet  zmath  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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