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Tangent spaces of the Teichmüller space of the torus with Thurston's weak metric

Abstract : In this paper, we show that the analogue of Thurston's asymmetric metric on the Teichmüller space of flat structures on the torus is weak Finsler and we give a geometric description of its unit sphere at each point in the tangent space to Teichmüller space. We then introduce a family of weak Finsler metrics which interpolate between Thurston's asymmetric metric and the Teichmüller metric of the torus (which coincides with the the hyperbolic metric). We describe the infinitesimal unit spheres of the metrics in this family. The final version of this paper will appear in Ann. Acad. Scien. Fennicae, Mathematica.
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https://hal.archives-ouvertes.fr/hal-02570185
Contributor : Athanase Papadopoulos <>
Submitted on : Friday, September 3, 2021 - 10:15:22 PM
Last modification on : Wednesday, September 8, 2021 - 12:20:48 PM

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  • HAL Id : hal-02570185, version 2
  • ARXIV : 2005.05646

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Hideki Miyachi, Ken'Ichi Ohshika, Athanase Papadopoulos. Tangent spaces of the Teichmüller space of the torus with Thurston's weak metric. 2020. ⟨hal-02570185v2⟩

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