Ads Manifolds With Particles and Earthquakes on Singular Surfaces
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- Bonsante, F. & Schlenker, JM. Geom. Funct. Anal. (2009) 19: 41. doi:10.1007/s00039-009-0716-9
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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.