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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2017, Volume 298, Pages 139–143
DOI: https://doi.org/10.1134/S0371968517030104 (Mi tm3812) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On the Isotopy Problem for Quasiconformal Mappings

V. A. Zorich

Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991 Russia
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DOI: https://doi.org/10.1134/S0371968517030104
Abstract: The question of the isotopy of a quasiconformal mapping and its special aspects in dimension greater than $2$ are considered. It is shown that an arbitrary quasiconformal mapping of a ball has an isotopy to the identity map such that the coefficient of quasiconformality (dilatation) of the mapping varies continuously and monotonically. In contrast to the planar case, in dimension higher than $2$ such an isotopy is not possible in an arbitrary domain. Examples showing specific features of the multidimensional case are given. In particular, they show that even when such an isotopy exists, it is not always possible to perform an isotopy so that the coefficient of quasiconformality approaches $1$ monotonically at each point in the source domain.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00592-а
Ministry of Education and Science of the Russian Federation НШ-9110.2016.1
This work was supported by the Russian Foundation for Basic Research (project no. 17-01-00592-a) and by a grant of the President of the Russian Federation (project no. NSh-9110.2016.1).
Received: December 15, 2016
English version:
Proceedings of the Steklov Institute of Mathematics, 2017, Volume 298, Pages 129–132
DOI: https://doi.org/10.1134/S0081543817060104
Bibliographic databases:
Document Type: Article
UDC: 517.54+514.774
Language: Russian
Citation: V. A. Zorich, “On the Isotopy Problem for Quasiconformal Mappings”, Complex analysis and its applications, Collected papers. On the occasion of the centenary of the birth of Boris Vladimirovich Shabat, 85th anniversary of the birth of Anatoliy Georgievich Vitushkin, and 85th anniversary of the birth of Andrei Aleksandrovich Gonchar, Trudy Mat. Inst. Steklova, 298, MAIK Nauka/Interperiodica, Moscow, 2017, 139–143; Proc. Steklov Inst. Math., 298 (2017), 129–132
Citation in format AMSBIB
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\paper On the Isotopy Problem for Quasiconformal Mappings
\inbook Complex analysis and its applications
\bookinfo Collected papers. On the occasion of the centenary of the birth of Boris Vladimirovich Shabat, 85th anniversary of the birth of Anatoliy Georgievich Vitushkin, and 85th anniversary of the birth of Andrei Aleksandrovich Gonchar
\serial Trudy Mat. Inst. Steklova
\yr 2017
\vol 298
\pages 139--143
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    • This publication is cited in the following 1 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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