Ads Manifolds With Particles and Earthquakes on Singular Surfaces

We prove two related results. The first is an "earthquake theorem" for closed hyperbolic surfaces with cone singularities where the total angle is less than pi: any two such metrics in are connected by a unique left earthquake. The second result is that the space of "globally hyperbolic" AdS manifolds with "particles" - cone singularities (of given angle) along time-like lines - is parametrized by the product of two copies of the Teichmuller space with some marked points (corresponding to the cone singularities). The two statements are proved together.