2016/10/25 by Qiyu Chen, Jean‐Marc Schlenker, Chen, Qiyu +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometry and complex manifolds #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.1610.07852
openalex publication_date 2016/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that for any convex globally hyperbolic maximal (GHM) anti-de Sitter (AdS) 3-dimensional space-time N with particles (cone singularities of angles less than π along time-like curves), 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 \citeBBZ2. We also describe a parametrization of the space of convex GHM AdS metrics on a given manifold, with particles of given angles, by the product of two copies of the Teichmüller 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 π a number of results concerning landslides, which are smoother analogs of earthquakes sharing some of their key properties.