Hilbert metric and quasiconformal mappings
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917935888465920 |
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| author | Altinkaya, Sahsene Fujimura, Masayo Vuorinen, Matti |
| author_facet | Altinkaya, Sahsene Fujimura, Masayo Vuorinen, Matti |
| contents | We prove a functional identity between the Hilbert metric and the visual angle metric in the unit disk. The proof utilizes the Poincaré hyperbolic metric in terms of which both metrics can be expressed. This identity then yields sharp distortion results for quasiregular mappings and analytic functions, expressed in terms of the Hilbert metric. We also prove that Hilbert circles are, in fact, Euclidean ellipses. The proof makes use of computer algebra methods. In particular, Gröbner bases are used. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18109 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hilbert metric and quasiconformal mappings Altinkaya, Sahsene Fujimura, Masayo Vuorinen, Matti Complex Variables 30C62 We prove a functional identity between the Hilbert metric and the visual angle metric in the unit disk. The proof utilizes the Poincaré hyperbolic metric in terms of which both metrics can be expressed. This identity then yields sharp distortion results for quasiregular mappings and analytic functions, expressed in terms of the Hilbert metric. We also prove that Hilbert circles are, in fact, Euclidean ellipses. The proof makes use of computer algebra methods. In particular, Gröbner bases are used. |
| title | Hilbert metric and quasiconformal mappings |
| topic | Complex Variables 30C62 |
| url | https://arxiv.org/abs/2502.18109 |