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 π: 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.
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Received: June 2007, Revision: May 2008, Accepted: June 2008
F.B. was partially supported by the A.N.R. project GEODYCOS. J.-M.S. was partially supported by the A.N.R. programs RepSurf, 2006-09, ANR-06-BLAN-0311, GeomEinstein, 2006-09, 06-BLAN-0154, and FOG, 2007-10, ANR-07-BLAN-0251-01.
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Bonsante, F., Schlenker, JM. Ads Manifolds With Particles and Earthquakes on Singular Surfaces. Geom. Funct. Anal. 19, 41–82 (2009). https://doi.org/10.1007/s00039-009-0716-9
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DOI: https://doi.org/10.1007/s00039-009-0716-9