The volume of maximal globally hyperbolic Cauchy-compact anti-de Sitter 3-manifolds is at least π²|χ(M)|, attained if and only if M is Fuchsian.
Some open questions on anti-de Sitter geometry
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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 Teichm\"uller theory, as well as analogs in hyperbolic geometry.
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2026 1verdicts
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Minimizing the volume of globally hyperbolic anti-de Sitter 3-manifolds
The volume of maximal globally hyperbolic Cauchy-compact anti-de Sitter 3-manifolds is at least π²|χ(M)|, attained if and only if M is Fuchsian.