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.
Ahlfors, An Extension of Schwarz’s Lemma.Transactions of the American Mathe- matical Society43(1938), pp
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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.