An analogue of Koebe's theorem in metric spaces
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915941201215488 |
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| author | Sevost'yanov, Evgeny Targonskii, Valery Romash, Denys Ilkevych, Nataliya |
| author_facet | Sevost'yanov, Evgeny Targonskii, Valery Romash, Denys Ilkevych, Nataliya |
| contents | This paper is devoted to the study of mappings in metric spaces. We investigate mappings satisfying inverse moduli inequalities. We show that under certain conditions on these mappings, their definition domains and the spaces in which they act, the image of a ball under the mappings contains a ball of fixed radius, which corresponds to the statement of the Koebe theorem on one quarter. As consequences, we obtain corresponding results in the Sobolev and Orlicz-Sobolev classes defined in a certain domain of a Riemannian surface or factor space by the group of fractional-linear mappings of the unit ball. We also give consequences for manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_15093 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An analogue of Koebe's theorem in metric spaces Sevost'yanov, Evgeny Targonskii, Valery Romash, Denys Ilkevych, Nataliya Complex Variables 30C65 This paper is devoted to the study of mappings in metric spaces. We investigate mappings satisfying inverse moduli inequalities. We show that under certain conditions on these mappings, their definition domains and the spaces in which they act, the image of a ball under the mappings contains a ball of fixed radius, which corresponds to the statement of the Koebe theorem on one quarter. As consequences, we obtain corresponding results in the Sobolev and Orlicz-Sobolev classes defined in a certain domain of a Riemannian surface or factor space by the group of fractional-linear mappings of the unit ball. We also give consequences for manifolds. |
| title | An analogue of Koebe's theorem in metric spaces |
| topic | Complex Variables 30C65 |
| url | https://arxiv.org/abs/2509.15093 |