Some open questions on anti-de Sitter geometry

Abstract

We present a list of open questions on various aspects of AdS geometry, that is, the geometry of Lorentz spaces of constant curvature -1. When possible we point out relations with homogeneous spaces and discrete subgroups of Lie groups, to Teichmüller theory, as well as analogs in hyperbolic geometry.

arXiv commentNot a research article in the usual sense but rather a list of open questions. 19 pages

References in corpus (6)

• Minimal stretch maps between hyperbolic surfaces
• On the renormalized volume of hyperbolic 3-manifolds
• Maximally stretched laminations on geometrically finite hyperbolic manifolds
• Fixed points of compositions of earthquakes
• Collisions of particles in locally AdS spacetimes II Moduli of globally hyperbolic spaces
• The Weil-Petersson metric and the renormalized volume of hyperbolic 3-manifolds

Cited by in corpus (10)

• A Geometric transition from hyperbolic to anti de Sitter geometry
• Geometric transition from hyperbolic to anti-de Sitter structures in dimension four
• Crooked surfaces and anti-de Sitter geometry
• The Volume of complete anti-de Sitter 3-manifolds
• Volume and non-existence of compact Clifford-Klein forms
• Character varieties of a transitioning Coxeter 4-orbifold
• ADS 3-manifolds and Higgs bundles
• Prescribing metrics on the boundary of AdS 3-manifolds
• Constant mean curvature foliation of domains of dependence in $Ad{S}_3$
• On the volume of Anti-de Sitter maximal globally hyperbolic three-manifolds