On the extremal length of the hyperbolic metric
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918289493458944 |
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| author | Masai, Hidetoshi |
| author_facet | Masai, Hidetoshi |
| contents | For any closed hyperbolic Riemann surface $X$, we show that the extremal length of the Liouville current is determined solely by the topology of \(X\). This confirms a conjecture of Martínez-Granado and Thurston. We also obtain an upper bound, depending only on $X$, for the diameter of extremal metrics on $X$ with area one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12400 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the extremal length of the hyperbolic metric Masai, Hidetoshi Geometric Topology Complex Variables Primary 30F30, Secondary 30C70, 30F45, 32G15 For any closed hyperbolic Riemann surface $X$, we show that the extremal length of the Liouville current is determined solely by the topology of \(X\). This confirms a conjecture of Martínez-Granado and Thurston. We also obtain an upper bound, depending only on $X$, for the diameter of extremal metrics on $X$ with area one. |
| title | On the extremal length of the hyperbolic metric |
| topic | Geometric Topology Complex Variables Primary 30F30, Secondary 30C70, 30F45, 32G15 |
| url | https://arxiv.org/abs/2505.12400 |