Geometric and Functional Analysis

, Volume 19, Issue 1, pp 41–82

Ads Manifolds With Particles and Earthquakes on Singular Surfaces

Article

DOI: 10.1007/s00039-009-0716-9

Cite this article as:
Bonsante, F. & Schlenker, JM. Geom. Funct. Anal. (2009) 19: 41. doi:10.1007/s00039-009-0716-9

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.

Keywords and phrases:

Earthquakescone singularitiesAdS geometry

AMS Mathematics Subject Classification:

32G1553C5030F1030F4530F60

Copyright information

© Birkhäuser Verlag, Basel 2009

Authors and Affiliations

  1. 1.Università degli Studi di PaviaPaviaItaly
  2. 2.Institut de Mathématiques de Toulouse, UMR CNRS 5219Toulouse cedex 9France