On boundary extension of mappings in metric spaces in terms of prime ends

Abstract

We study the boundary behavior of the so-called ring $Q$-mappings obtained as a natural generalization of mappings with bounded distortion. We establish a series of conditions imposed on a function $Q(x)$ for the continuous extension of given mappings with respect to prime ends in domains with regular boundaries in metric spaces.

arXiv commentarXiv admin note: text overlap with arXiv:1204.6444, arXiv:1608.02393 by other authors

References in corpus (1)

• Prime ends in metric spaces and boundary extensions of mappings