Geodesic
Differential properties of mappings with $s$-average characteristic
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 1, Tome 199 (2021), pp. 80-85
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In this paper, we develop the geometric method of moduli of curve families and consider the problem of differential properties of nonhomeomorphic mappings with $s$-averaged characteristic. These properties can be applied in the theory of multidimensional quasiconformal mappings and their generalizations. We prove that if $f$ is an extremal mapping with $s$-averaged characteristic, then it belongs to the class $W^2_2$.
Keywords: homeomorphism, mapping, characteristic, distortion, module of a family of curves. 
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A. N. Malyutina; U. K. Asanbekov; A. V. Novik. Differential properties of mappings with $s$-average characteristic. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 1, Tome 199 (2021), pp. 80-85. http://geodesic.mathdoc.fr/item/INTO_2021_199_a8/

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