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

Abstract

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

12 pages, identical to the version appeared online on Rendiconti di Matematica e delle sue Applicazioni (May 2026)