CONSTANT GAUSS CURVATURE FOLIATIONS OF ADS SPACETIMES WITH PARTICLES

We prove that for any convex globally hyperbolic compact maximal (GHCM) anti-de Sitter (AdS) 3-dimensional spacetime N with particles (cone singularities of angles less than p along time-like lines), the complement of the convex core in N admits a unique foliation by constant Gauss curvature surfaces. This extends and provides a new proof of a result of Barbot, Beguin, and Zeghib. We also describe a parametrization of the space of convex GHCM AdS metrics on a given manifold, with particles of given angles, by the product of two copies of the Teichmuller space of hyperbolic metrics with cone singularities of fixed angles. Finally, we use the results on K-surfaces to extend to hyperbolic surfaces with cone singularities of angles less than p a number of results concerning landslides, which are smoother analogs of earthquakes sharing some of their key properties.