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 $R^n$, $n\geqslant3$. 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.
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