Titlebook: Mappings with Direct and Inverse Poletsky Inequalities; Evgeny Sevost‘yanov Book 2023 The Editor(s) (if applicable) and The Author(s), und

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On Boundary Extension of Mappings in Metric Spaces in Terms of Prime Ends,m of a continuous boundary extension of the corresponding inverse mappings. In addition, we have obtained theorems on the equicontinuity of families of ring .-mappings in the closure of a domain by prime ends. We have constructed examples of both mappings and concrete metric spaces that satisfy the conditions of the main results.

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Boundary Behavior of Mappings with Poletsky Inequality,main result of the chapter. In what follows, we formulate this result in the form of an extremely general lemma, which is given in terms of the so-called singular parameters. The main result of the chapter is formulated in the form of theorems containing FMO-type conditions and integral-type conditions.

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On the Openness and Discreteness of Mappings with the Inverse Poletsky Inequality,obtain discreteness and openness of such mappings under appropriate conditions. At the same time, the main result of the chapter is proved in the form of a lemma formulated in terms of singular parameters.

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