arXiv math/06091162006-09math.GTmath.DG

AdS manifolds with particles and earthquakes on singular surfaces

Francesco Bonsante, Jean-Marc Schlenker

备注：: 18 pages, several figures. v2: improved exposition, several corrections

英文摘要：

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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