Convergence of earthquake and horocycle paths to the boundary of Teichmüller space

Manman Jiang; Weixu Su

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arXiv · 1512.08664

Convergence of earthquake and horocycle paths to the boundary of Teichmüller space

Manman Jiang·Weixu Su

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Abstract

We study the convergence of earthquake paths and horocycle paths in the Gardiner-Masur compactification of Teichmüller space. We show that an earthquake path directed by a uniquely ergodic or simple closed measured geodesic lamination converges to the Gardiner-Masur boundary. Using the embedding of flat metrics into the space of geodesic currents, we prove that a horocycle path in Teichmüller space, induced by a quadratic differential whose vertical measured foliation is unique ergodic, converges to the Gardiner-Masur boundary and to the Thurston boundary.

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BibTeX RIS

Manman Jiang, Weixu Su. 2015-12-29. Convergence of earthquake and horocycle paths to the boundary of Teichmüller space. https://arxiv.org/abs/1512.08664

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