Convex surfaces with prescribed induced metrics in anti-de Sitter spacetimes

2024/05/03 by Qiyu Chen, Jean‐Marc Schlenker, Chen, Qiyu +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT)

paper · pdf · doi:10.48550/arxiv.2405.01912

openalex publication_date 2024/05/03 · openalex created_date 2024/05/10 · openalex updated_date 2026/07/28

Abstract

Let S be a closed surface of genus at least 2, let h be a smooth metric of curvature K<-1 on S, and let h₀ be a hyperbolic metric on S. We show that there exists a unique quasifuchsian AdS spacetime with left metric isotopic to h₀, containing a past-convex Cauchy surface with induced metric isotopic to h.

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