On lower distance estimates of mappings in metric spaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915007515590656 |
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| author | Sevost'yanov, Evgeny Romash, Denys Ilkevych, Nataliya |
| author_facet | Sevost'yanov, Evgeny Romash, Denys Ilkevych, Nataliya |
| contents | We consider mappings satisfying an upper bound for the distortion of families of curves. We establish lower bounds for the distortion of distances under such mappings. As applications, we obtain theorems on the discreteness of the limit mapping of a sequence of mappings converging locally uniformly. We separately consider cases when mappings are defined in Euclidean $n$-dimensional space and in a metric space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03775 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On lower distance estimates of mappings in metric spaces Sevost'yanov, Evgeny Romash, Denys Ilkevych, Nataliya Complex Variables 30C65 We consider mappings satisfying an upper bound for the distortion of families of curves. We establish lower bounds for the distortion of distances under such mappings. As applications, we obtain theorems on the discreteness of the limit mapping of a sequence of mappings converging locally uniformly. We separately consider cases when mappings are defined in Euclidean $n$-dimensional space and in a metric space. |
| title | On lower distance estimates of mappings in metric spaces |
| topic | Complex Variables 30C65 |
| url | https://arxiv.org/abs/2411.03775 |