On prime ends on Riemannian manifolds


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We study the boundary behavior of the classes of ring mappings on Riemannian manifolds, which are a generalization of quasiconformal mappings by Gehring. In terms of the prime ends of regular domains, the theorems of continuous extension of those classes onto the boundary of a domain are presented.

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Denis Ilyutko

Chair of Differential Geometry and Applications, Mechanico-Mathematical Faculty, M. V. Lomonosov Moscow State University

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Email: ilyutko@yandex.ru
俄罗斯联邦, Moscow

Evgeny Sevost’yanov

I. Franko Zhytomyr State University; Institute of Applied Mathematics and Mechanics of the NAS of Ukraine

Email: ilyutko@yandex.ru
乌克兰, Zhytomyr; Slavyansk

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