Prescribing metrics on the boundary of AdS 3-manifolds

Abstract

We prove that given two metrics $g_{+}$ and $g_{-}$ with curvature $\kappa <-1$ on a closed, oriented surface $S$ of genus $\tau \ge 2$, there exists an $AdS$ manifold $N$ with smooth, space-like, strictly convex boundary such that the induced metrics on the two connected components of $\partial N$ are equal to $g_{+}$ and $g_{-}$. Using the duality between convex space-like surfaces in $Ad{S}_3$, we obtain an equivalent result about the prescription of the third fundamental form.

27 pages. Final version

References in corpus (2)

• Prescribing metrics on the boundary of convex cores of globally hyperbolic maximal compact AdS 3-manifolds
• Some open questions on anti-de Sitter geometry

Cited by in corpus (1)

• Constant mean curvature foliation of globally hyperbolic (2+1)-spacetimes with particles