Realizing metrics of curvature ≤ -1 on closed surfaces in Fuchsian anti-de Sitter manifolds

2019/11/06 by Hicham Labeni, Labeni, Hicham
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1912.03123

openalex publication_date 2019/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that any metric with curvature ≤ -1 (in the sense of A. D. Alexandrov) on a closed surface of genus >1 is isometric to the induced intrinsic metric on a space-like convex surface in a Lorentzian manifold of dimension (2+1) with sectional curvature -1. The proof is done by approximation, using a result about isometric immersion of smooth metrics by Labourie--Schlenker.

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• Compact domains with prescribed convex boundary metrics in quasi-Fuchsian manifolds
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