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arXiv · 1709.06834

Geodesics Currents and Counting Problems

Kasra Rafi·Juan Souto
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Abstract

For every positive, continuous and homogeneous function $f$ on the space of currents on a compact surface $\overlineΣ$, and for every compactly supported filling current $α$, we compute as $L \to \infty$, the number of mapping classes $ϕ$ so that $f(ϕ(α))\leq L$. As an application, when the surface in question is closed, we prove a lattice counting theorem for Teichmüller space equipped with the Thurston metric.

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Kasra Rafi, Juan Souto. 2019-03-23. Geodesics Currents and Counting Problems. https://arxiv.org/abs/1709.06834

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