On the Theory of Prime Ends for Space Mappings

  • D. A. Kovtonyuk Ин-т прикл. математики и механики НАН Украины, Донецк
  • V. I. Ryazanov Ин-т прикл. математики и механики НАН Украины, Донецк

Abstract

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.
Published
25.04.2015
How to Cite
KovtonyukD. A., and RyazanovV. I. “On the Theory of Prime Ends for Space Mappings”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 4, Apr. 2015, pp. 467-79, http://umj.imath.kiev.ua/index.php/umj/article/view/1997.
Section
Research articles