AdS manifolds with particles and earthquakes on singular surfaces

Francesco Bonsante; Jean-Marc Schlenker

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arXiv · math/0609116

AdS manifolds with particles and earthquakes on singular surfaces

Francesco Bonsante·Jean-Marc Schlenker

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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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Francesco Bonsante, Jean-Marc Schlenker. 2007-06-18. AdS manifolds with particles and earthquakes on singular surfaces. https://arxiv.org/abs/math/0609116

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