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, which is 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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Jiang, M., Su, W. Convergence of earthquake and horocycle paths to the boundary of Teichmüller space. Sci. China Math. 59, 1937–1948 (2016). https://doi.org/10.1007/s11425-016-5138-1
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DOI: https://doi.org/10.1007/s11425-016-5138-1