On Caratheodory theorem for open discrete unclosed mappings

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Kovba, Zarina, Sevost'yanov, Evgeny
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866915918200700928
author Kovba, Zarina
Sevost'yanov, Evgeny
author_facet Kovba, Zarina
Sevost'yanov, Evgeny
contents We study mappings satisfying the inverse Poletsky-type inequality in a domain of the Euclidean space. Such inequalities are well known and play an important role in the study of quasiconformal and quasiregular mappings. We consider the case when the mapped domain, generally speaking, is not locally connected on its boundary. At the same time, we consider the situation when the mapping is open and discrete, but may not preserve the boundary of the domain. In terms of prime ends, we obtain results on the equicontinuity of families of such mappings in the closure of the definition domain. As a consequence, we also obtain the corresponding statement for Orlicz-Sobolev classes.
format Preprint
id arxiv_https___arxiv_org_abs_2502_16209
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On Caratheodory theorem for open discrete unclosed mappings
Kovba, Zarina
Sevost'yanov, Evgeny
Complex Variables
30C65, 31A15, 31B25
We study mappings satisfying the inverse Poletsky-type inequality in a domain of the Euclidean space. Such inequalities are well known and play an important role in the study of quasiconformal and quasiregular mappings. We consider the case when the mapped domain, generally speaking, is not locally connected on its boundary. At the same time, we consider the situation when the mapping is open and discrete, but may not preserve the boundary of the domain. In terms of prime ends, we obtain results on the equicontinuity of families of such mappings in the closure of the definition domain. As a consequence, we also obtain the corresponding statement for Orlicz-Sobolev classes.
title On Caratheodory theorem for open discrete unclosed mappings
topic Complex Variables
30C65, 31A15, 31B25
url https://arxiv.org/abs/2502.16209