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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.19736 |
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| _version_ | 1866910428998664192 |
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| author | Dong, Xinlong Šarić, Dragomir Wang, Zhe |
| author_facet | Dong, Xinlong Šarić, Dragomir Wang, Zhe |
| contents | The Liouville map, introduced by Bonahon, assigns to each point in the Teichmüller space a natural Radon measure on the space of geodesics of the base surface. The Liouville map is real analytic and it even extends to a holomorphic map of a neighborhood of the Teichmüller space in the Quasi-Fuchsian space of an arbitrary conformally hyperbolic Riemann surface. The earthquake paths and by their extension quake-bends, introduced by Thurston, are particularly nice real-analytic and holomorphic paths in the Teichmüller and the Quasi-Fuchsian space, respectively. We find a geometric expression for the derivative of the Liouville map along earthquake paths. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19736 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the derivatives of the Liouville currents Dong, Xinlong Šarić, Dragomir Wang, Zhe Complex Variables The Liouville map, introduced by Bonahon, assigns to each point in the Teichmüller space a natural Radon measure on the space of geodesics of the base surface. The Liouville map is real analytic and it even extends to a holomorphic map of a neighborhood of the Teichmüller space in the Quasi-Fuchsian space of an arbitrary conformally hyperbolic Riemann surface. The earthquake paths and by their extension quake-bends, introduced by Thurston, are particularly nice real-analytic and holomorphic paths in the Teichmüller and the Quasi-Fuchsian space, respectively. We find a geometric expression for the derivative of the Liouville map along earthquake paths. |
| title | On the derivatives of the Liouville currents |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2404.19736 |