Gespeichert in:
| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2404.19736 |
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Inhaltsangabe:
- 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.