AdS manifolds with particles and earthquakes on singular surfaces

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 $\pi$: 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.

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

References in corpus (1)

• Lorentz spacetimes of constant curvature

Cited by in corpus (2)

• Notes on a paper of Mess
• Gauss images of hyperbolic cusps with convex polyhedral boundary