Some remarks on bounded earthquakes

Šarić, Dragomir

doi:10.1090/S0002-9939-09-10156-9

Some remarks on bounded earthquakes
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Proc. Amer. Math. Soc. 138 (2010), 871-879 Request permission

Abstract:

We show that an earthquake of a geometrically infinite hyperbolic surface induces an asymptotically conformal change in the hyperbolic metric if and only if the measured lamination associated with the earthquake is asymptotically trivial on the surface. Then we show that the contraction along earthquake paths is continuous in the Teichmüller space of any hyperbolic surface. Finally, we show that if a measured lamination vanishes while approaching infinity at a rate higher than the distance to the boundary, then it must be trivial.

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