反德西特时空中具有规定诱导度量的凸曲面

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2024-11-17 DOI:10.1112/blms.13189

Qiyu Chen, Jean-Marc Schlenker

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引用次数: 0

摘要

设S$ S$是一个至少为2的闭曲面，设h$ h$是曲率K <的光滑度规；−1$ K<-1$在S$ S$上，设h 0$ h_0$为S$ S$上的双曲度规。我们证明了存在一个左度量同位素为h0 $h_0$的唯一的准紫红色AdS时空，它包含一个诱导度量同位素为h$ h$的过去凸柯西曲面。

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

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 $h$ .