On boundary behavior of mappings on Riemannian manifolds in terms of prime ends

2017/05/07 by Ilyutko, D. P., Sevost'yanov, E. A.
#30C65 #30L10 #58C06 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.02710

Abstract

A boundary behavior of ring mappings on Riemannian manifolds, which are generalization of quasiconformal mappings by Gehring, is investigated. In terms of prime ends, there are obtained theorems about continuous extension to a boundary of classes mentioned above. In the terms mentioned above, there are obtained results about equicontinuity of these classes in the closure of the domain.

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