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

Chen, Qiyu; Schlenker, Jean-Marc

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Preprint

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

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Schlenker, Jean-Marc
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.48550/arXiv.2405.01912
(プレプリント)

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2405.01912.pdf
(プレプリント), 217KB

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引用

Chen, Q., & Schlenker, J.-M. (submitted). Convex surfaces with prescribed induced metrics in anti-de Sitter spacetimes.

引用: https://hdl.handle.net/21.11116/0000-000F-59FC-2

要旨

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.