Analytic mappings of the unit disk with bounded compression
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912493317652480 |
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| author | Ivrii, Oleg Nicolau, Artur |
| author_facet | Ivrii, Oleg Nicolau, Artur |
| contents | In this paper, we study analytic self-maps of the unit disk for which the hyperbolic diameters of the images of hyperbolic balls of radius 1 are uniformly bounded below. We give several characterizations of such maps involving the behaviour along geodesic rays, Aleksandrov-Clark measures, zero sets and critical sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15200 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analytic mappings of the unit disk with bounded compression Ivrii, Oleg Nicolau, Artur Complex Variables Classical Analysis and ODEs 30J05, 30F45, 30H20, 30C80 In this paper, we study analytic self-maps of the unit disk for which the hyperbolic diameters of the images of hyperbolic balls of radius 1 are uniformly bounded below. We give several characterizations of such maps involving the behaviour along geodesic rays, Aleksandrov-Clark measures, zero sets and critical sets. |
| title | Analytic mappings of the unit disk with bounded compression |
| topic | Complex Variables Classical Analysis and ODEs 30J05, 30F45, 30H20, 30C80 |
| url | https://arxiv.org/abs/2507.15200 |