Abstract:
With the concept of the variational p-capacity of a condenser as a starting point, the mean inner and outer deviations are defined for homeomorphic mappings of bounded domains in Rn, n⩾3. Analytic expressions which are integral means of the usual analytic deviations of a homeomorphism are established for such deviations. Various equivalent geometric and analytic definitions are given for mappings quasiconformal in the mean and for quasiconformal mappings. An estimate is determined for the distortion of Euclidean distances under mappings quasiconformal in the mean and other mappings.
Bibliography: 14 titles.
\Bibitem{Kru86}
\by V.~I.~Kruglikov
\paper Capacity of condensers and spatial mappings quasiconformal in the mean
\jour Math. USSR-Sb.
\yr 1987
\vol 58
\issue 1
\pages 185--205
\mathnet{http://mi.mathnet.ru/eng/sm1864}
\crossref{https://doi.org/10.1070/SM1987v058n01ABEH003099}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=854971}
\zmath{https://zbmath.org/?q=an:0619.30025}
Linking options:
https://www.mathnet.ru/eng/sm1864
https://doi.org/10.1070/SM1987v058n01ABEH003099
https://www.mathnet.ru/eng/sm/v172/i2/p185
This publication is cited in the following 64 articles:
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Vladimir Gol'dshtein, Alexander Ukhlov, “On the functional properties of weak (p,q)-quasiconformal homeomorphisms”, UMB, 16:3 (2019), 329
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