AdS manifolds with particles and earthquakes on singular surfaces

We prove an ``Earthquake theorem'' for closed hyperbolic surfaces with cone
singularities where the total angle is less than $\pi$: the action of the
space of measured laminations on Teichm\"uller space by left earthquakes is
simply transitive. This is strongly related to another result: the space of
``globally hyperbolic'' AdS manifolds with cone singularities along time-like
geodesics is parametrized by the product two copies of Teichm\"uller space with
some marked points (corresponding to the cone singularities).