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arXiv · 1505.06695

Limits of Teichm\"uller geodesics in the Universal Teichm\"uller space

Hrant Hakobyan·Dragomir Saric
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Abstract

Thurston's boundary to the universal Teichm\"uller space $T(\mathbb{H})$ is the set of asymptotic rays to the embedding of $T(\mathbb{H})$ in the space of geodesic currents; the boundary is identified with the projective bounded measured laminations $PML_{bdd}(\mathbb{H})$ of $\mathbb{H}$. We prove that each Teichm\"uller geodesic ray in $T(\mathbb{H})$ has a unique limit point in Thurston's boundary to $T(\mathbb{H})$ unlike in the case of closed surfaces.

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Hrant Hakobyan, Dragomir Saric. 2015-05-25. Limits of Teichm\"uller geodesics in the Universal Teichm\"uller space. https://doi.org/10.1112/plms.12125

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