Thurston's boundary to infinite-dimensional Teichm\"uller spaces: geodesic currents

Dragomir Saric

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arXiv · 1505.01099

Thurston's boundary to infinite-dimensional Teichm\"uller spaces: geodesic currents

Dragomir Saric

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Abstract

Let $X_0$ be a complete borderless infinite area hyperbolic surface. We introduce Thurston's boundary to the Teichm\"uller space $T(X_0)$ of the surface $X_0$ using Liouville (geodesic) currents. Thurston's boundary to $T(X_0)$ is identified with the space $PML_{bdd}(X_0)$ of projective bounded measured laminations on $X_0$ which naturally extends Thurston's result for closed surfaces. Moreover, the quasiconformal mapping class group $MCG_{qc}(X_0)$ acts continuously on the closure $T(X_0)\cup PML_{bdd}(X_0)$.

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Dragomir Saric. 2015-05-05. Thurston's boundary to infinite-dimensional Teichm\"uller spaces: geodesic currents. https://arxiv.org/abs/1505.01099

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