Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 44, 2019, 65-90

ON BOUNDARY EXTENSION OF MAPPINGS IN METRIC SPACES IN THE TERMS OF PRIME ENDS

Evgeny Sevost'yanov

Zhytomyr Ivan Franko State University
40 Bol'shaya Berdichevskaya Str., 10 008 Zhytomyr, Ukraine; esevostyanov2009 'at' gmail.com

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.

2010 Mathematics Subject Classification: Primary 30L10; Secondary 30C65.

Key words: Mappings with finite and bounded distortion, prime ends, metric spaces, boundary behavior.

Reference to this article: E. Sevost'yanov: On boundary extension of mappings in metric spaces in the terms of prime ends. Ann. Acad. Sci. Fenn. Math. 44 (2019), 65-90.

Full document as PDF file

https://doi.org/10.5186/aasfm.2019.4405