Reference : Constant Gauss curvature foliations of AdS spacetimes with particles
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Constant Gauss curvature foliations of AdS spacetimes with particles
Schlenker, Jean-Marc mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
chen, qiyu []
In press
Transactions of the American Mathematical Society
American Mathematical Society
United States
[en] 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 \cite{BBZ2}. 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 Teichm\"uller 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.
university of luxembourg: mathematics research unit

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