2025/10/10 by Роман Просанов, Prosanov, Roman
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2510.09313
We first prove that given a Fuchsian representation ρ_∘: π1S \ra \rm PSL(2,\R), where S is a closed oriented surface of genus ≥ 2, any hyperbolic cone-metric on S with cone-angles >2π isometrically embeds as a future-convex bent Cauchy surface in a globally hyperbolic maximal Cauchy compact (GHMC) anti-de Sitter (2+1)-spacetime whose left representation is ρ_∘. Second, we show that given any two such cone-metrics, there exists a GHMC anti-de Sitter (2+1)-spacetime in which the cone-metrics embed simultaneously, one as a future-convex bent Cauchy surface and one as a past-convex. Furthermore, in both cases we establish that such a spacetime and embeddings are unique provided that the cone-metrics are sufficiently small.