Coarse and fine geometry of the Thurston metric

David Dumas; Anna Lenzhen; Kasra Rafi; Jing Tao

doi:10.1017/fms.2020.3

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arXiv · 1610.07409

Coarse and fine geometry of the Thurston metric

David Dumas·Anna Lenzhen·Kasra Rafi·Jing Tao

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Abstract

We study the geometry of the Thurston metric on the Teichmüller space $\mathcal{T}(S)$ of hyperbolic structures on a surface $S$. Some of our results on the coarse geometry of this metric apply to arbitrary surfaces $S$ of finite type; however, we focus particular attention on the case where the surface is a once-punctured torus, $S_{1,1}$. In that case, our results provide a detailed picture of the infinitesimal, local, and global behavior of the geodesics of the Thurston metric, as well as an analogue of Royden's theorem.

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BibTeX RIS

David Dumas, Anna Lenzhen, Kasra Rafi, Jing Tao. 2019-12-30. Coarse and fine geometry of the Thurston metric. https://doi.org/10.1017/fms.2020.3

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