AdS manifolds with particles and earthquakes on singular surfaces

Abstract. 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 Teichmüller space with some marked points (corresponding to the cone singularities). The two statements are proved together. 1. Introduction an