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Equicontinuity and Isolated Singularities of Mappings with the Inverse Poletsky Inequality

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Mappings with Direct and Inverse Poletsky Inequalities

Part of the book series: Developments in Mathematics ((DEVM,volume 78))

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Abstract

The results of this chapter were obtained together with S. Skvortsov. The chapter investigates mappings whose inverses distort the modulus of paths similarly to the Poletsky inequality. In other words, here we study homeomorphisms with the inverse Poletsky inequality, which may be interpreted as mappings inverse to ring Q-homeomorphisms. We study here the case when the function Q is simply integrable in the corresponding domain. It is proved that, the classes of such homeomorphisms form equicontinuous families. Under additional conditions on the geometry of the definition and the image domains, these families are equicontinuous not only at inner but also at boundary points. In addition, the problem of removability of the isolated singularities for such mappings is resolved.

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Authors and Affiliations

  1. Mathematical Analysis, Business Analysis and Statistics Department, Zhytomyr Ivan Franko State University, Zhytomyr, Ukraine

    Evgeny Sevost’yanov

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  1. Evgeny Sevost’yanov
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Sevost’yanov, E. (2023). Equicontinuity and Isolated Singularities of Mappings with the Inverse Poletsky Inequality. In: Mappings with Direct and Inverse Poletsky Inequalities. Developments in Mathematics, vol 78. Springer, Cham. https://doi.org/10.1007/978-3-031-45418-9_11

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