On Caratheodory theorem for open discrete unclosed mappings
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| 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 |