On the prime ends extension of unclosed inverse mappings
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913491926908928 |
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| author | Sevost'yanov, Evgeny Kovba, Victoria Desyatka Zarina |
| author_facet | Sevost'yanov, Evgeny Kovba, Victoria Desyatka Zarina |
| contents | We consider mappings that distort the modulus of families of paths in the opposite direction in the manner of Poletsky's inequality. Here we study the case when the mappings are not closed, in particular, they do not preserve the boundary of the domain under the mapping. Under certain conditions, we obtain results on the continuous boundary extension of such mappings in the sense of prime ends. In addition, we obtain corresponding results on the equicontinuity of families of such mappings in terms of prime ends. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02956 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the prime ends extension of unclosed inverse mappings Sevost'yanov, Evgeny Kovba, Victoria Desyatka Zarina Complex Variables 30C65, 31A15, 31B25 We consider mappings that distort the modulus of families of paths in the opposite direction in the manner of Poletsky's inequality. Here we study the case when the mappings are not closed, in particular, they do not preserve the boundary of the domain under the mapping. Under certain conditions, we obtain results on the continuous boundary extension of such mappings in the sense of prime ends. In addition, we obtain corresponding results on the equicontinuity of families of such mappings in terms of prime ends. |
| title | On the prime ends extension of unclosed inverse mappings |
| topic | Complex Variables 30C65, 31A15, 31B25 |
| url | https://arxiv.org/abs/2409.02956 |