Masur's criterion does not hold in the Thurston metric

Ivan Telpukhovskiy

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arXiv · 1903.00845

Masur's criterion does not hold in the Thurston metric

Ivan Telpukhovskiy

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Abstract

We construct a counterexample for an analogue of Masur's criterion in the setting of Teichm\"uller space equipped with the Thurston metric. For that, we find a minimal, filling, non-uniquely ergodic lamination $\lambda$ on the seven-times punctured sphere with uniformly bounded annular projection distances. Then we show that a geodesic in the corresponding Teichm\"uller space that converges to $\lambda$, stays in the thick part for the whole time.

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Ivan Telpukhovskiy. 2019-03-03. Masur's criterion does not hold in the Thurston metric. https://arxiv.org/abs/1903.00845

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