Prescribing Metrics on the Boundary of Anti-de Sitter 3-Manifolds

Abstract

We prove that given two metrics g+ and g− with curvature � < 1 on a closed, oriented surface S of genus � � 2, there exists an AdS3 manifold N with smooth, space-like, strictly convex boundary such that the induced metrics on the two connected components of @N are equal to g+ and g−. Using the duality between convex space-like surfaces in AdS3, we obtain an equivalent result about the prescription of the third fundamental form. This answers partially Question 3.5 in (BBD+12).