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

Qiyu Chen; Jean-Marc Schlenker

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arXiv · 2405.01912

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

Qiyu Chen·Jean-Marc Schlenker

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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 $h_0$ be a hyperbolic metric on $S$. We show that there exists a unique quasifuchsian AdS spacetime with left metric isotopic to $h_0$, containing a past-convex Cauchy surface with induced metric isotopic to $h$.

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Qiyu Chen, Jean-Marc Schlenker. 2024-05-03. Convex surfaces with prescribed induced metrics in anti-de Sitter spacetimes. https://arxiv.org/abs/2405.01912

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