We study the geometry of a general class of vacuum asymptotically Anti-de Sitter spacetimes near the conformal boundary. In particular, the spacetime is only assumed to have finite regularity, and it is allowed to have arbitrary boundary topology and geometry. For the main results, we derive limits at the conformal boundary of various geometric quantities, and we use these limits to construct partial Fefferman--Graham expansions from the boundary. The results of this article will be applied, in upcoming papers, toward proving symmetry extension and gravity--boundary correspondence theorems for vacuum asymptotically Anti-de Sitter spacetimes.

中文翻译：

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爱因斯坦真空渐近反德西特时空的近边界几何

我们研究了共形边界附近的一类真空渐近反德西特时空的几何形状。特别地，时空仅被假定为具有有限规律性，并且允许具有任意边界拓扑和几何形状。对于主要结果，我们推导出各种几何量的共形边界处的极限，并使用这些极限从边界构造部分 Fefferman--Graham 展开。本文的结果将在即将发表的论文中用于证明真空渐近反德西特时空的对称扩展和重力边界对应定理。