We study the convergence of earthquake paths and horocycle paths in the Gardiner-Masur compact- ification of Teichmfiller space. We show that an earthquake path directed by a uniquely ergodic or simple closed measured...We study the convergence of earthquake paths and horocycle paths in the Gardiner-Masur compact- ification of Teichmfiller 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 Teichmiiller space, which is induced by a quadratic differential whose vertical measured foliation is uniquely ergodic, converges to the Gardiner-Masur boundary and to the Thurston boundary.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11271378 and 11201078)
文摘We study the convergence of earthquake paths and horocycle paths in the Gardiner-Masur compact- ification of Teichmfiller 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 Teichmiiller space, which is induced by a quadratic differential whose vertical measured foliation is uniquely ergodic, converges to the Gardiner-Masur boundary and to the Thurston boundary.
