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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.02008 |
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| _version_ | 1866914430828150784 |
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| author | Sevost'yanov, Evgeny Targonskii, Valery Ilkevych, Nataliya |
| author_facet | Sevost'yanov, Evgeny Targonskii, Valery Ilkevych, Nataliya |
| contents | We study mappings that satisfy the inverse modulus inequality of Poletsky type with respect to $p$-modulus. Given $n-1<p\leqslant n,$ we show that, the image of some ball contains a fixed ball under mappings mentioned above. This statement can be interpreted as the well-known analogue of Koebe's theorem for analytic functions. As a consequence, we obtain the openness and discreteness of the limit mapping in the class under study. The paper also studies mappings of the Orlicz-Sobolev classes, for which an analogue of the Koebe one-quarter theorem is obtained as a consequence of the main results |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02008 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Koebe's theorem for mappings with integral constraints Sevost'yanov, Evgeny Targonskii, Valery Ilkevych, Nataliya Complex Variables 30C65 We study mappings that satisfy the inverse modulus inequality of Poletsky type with respect to $p$-modulus. Given $n-1<p\leqslant n,$ we show that, the image of some ball contains a fixed ball under mappings mentioned above. This statement can be interpreted as the well-known analogue of Koebe's theorem for analytic functions. As a consequence, we obtain the openness and discreteness of the limit mapping in the class under study. The paper also studies mappings of the Orlicz-Sobolev classes, for which an analogue of the Koebe one-quarter theorem is obtained as a consequence of the main results |
| title | On Koebe's theorem for mappings with integral constraints |
| topic | Complex Variables 30C65 |
| url | https://arxiv.org/abs/2509.02008 |