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

TL;DR

This paper proves a lower bound on the volume of certain 3-manifolds in anti-de Sitter space, showing the minimum is achieved by Fuchsian manifolds, linking geometry and topology.

Contribution

It establishes a sharp volume bound for maximal globally hyperbolic anti-de Sitter 3-manifolds and characterizes the case of equality.

Findings

Volume of such manifolds is at least π² times the absolute Euler characteristic.

The minimum volume is attained precisely by Fuchsian manifolds.

Provides a geometric characterization of volume minimizers.

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.