Degeneration of globally hyperbolic maximal anti-de Sitter structures along pinching sequences

Abstract

Let $S$ be a closed oriented surface of genus at least $2$. Using the parameterisation of the deformation space of globally hyperbolic maximal anti-de Sitter structures on $S \times \mathbb{R}$ by the cotangent bundle over the Teichm\"uller space of $S$, we study the behaviour of these geometric structures along pinching sequences. We show, in particular, that the regular globally hyperbolic anti-de Sitter structures introduced in arXiv:1806.08176 naturally appear as limiting points.