Minimizing the volume of globally hyperbolic anti-de Sitter 3-manifolds

In this paper we show that the volume of a maximal globally hyperbolic Cauchy-compact anti-de Sitter $3$-manifold $M$ is at least ${\pi }^2\mathrm{\mid }\chi (M)\mathrm{\mid }$, and that this minimum value is attained if and only if $M$ is Fuchsian.