On the Theory of Prime Ends for Space Mappings

We present a canonical representation of prime ends in regular domains and, on this basis, study the boundary behavior of the so-called lower Q -homeomorphisms obtained as a natural generalization of quasiconformal mappings. We establish a series of effective conditions imposed on a function Q ( x )...

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Bibliographic Details
Published inUkrainian mathematical journal Vol. 67; no. 4; pp. 528 - 541
Main Authors Kovtonyuk, D. A., Ryazanov, V. I.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.09.2015
Springer
Subjects
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
Statistics
Boundary Behavior
Borel Function
Quasiconformal Mapping
Canonical Representation
Sobolev Class
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Summary:We present a canonical representation of prime ends in regular domains and, on this basis, study the boundary behavior of the so-called lower Q -homeomorphisms obtained as a natural generalization of quasiconformal mappings. We establish a series of effective conditions imposed on a function Q ( x ) for the homeomorphic extension of given mappings with respect to prime ends in domains with regular boundaries. The developed theory is applicable, in particular, to mappings of the Orlicz–Sobolev classes and also to finitely bi-Lipschitz mappings, which can be regarded as a significant generalization of the well-known classes of isometric and quasiisometric mappings.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-015-1098-9