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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.09012 |
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| _version_ | 1866929358954823680 |
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| author | Sevost'yanov, Evgeny Targonskii, Valery |
| author_facet | Sevost'yanov, Evgeny Targonskii, Valery |
| contents | We study mappings that satisfy the inverse modulus inequality of Poletsky type in a fixed domain. It is shown that, under some additional restrictions, the image of a ball under such mappings contains a fixed ball uniformly over the class. This statement can be interpreted as the well-known analogue of Koebe's theorem for analytic functions. As an application of the obtained result, we show that, if a sequence of mappings belonging to the specified class converges locally uniformly, then the limit mapping is open. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09012 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An analogue of Koebe's theorem and the openness of a limit map in one class Sevost'yanov, Evgeny Targonskii, Valery Complex Variables 30C65 We study mappings that satisfy the inverse modulus inequality of Poletsky type in a fixed domain. It is shown that, under some additional restrictions, the image of a ball under such mappings contains a fixed ball uniformly over the class. This statement can be interpreted as the well-known analogue of Koebe's theorem for analytic functions. As an application of the obtained result, we show that, if a sequence of mappings belonging to the specified class converges locally uniformly, then the limit mapping is open. |
| title | An analogue of Koebe's theorem and the openness of a limit map in one class |
| topic | Complex Variables 30C65 |
| url | https://arxiv.org/abs/2405.09012 |