We prove that every proper n-dimensional length metric space admits an “approximate isometric embedding” into Lorentzian space ℝ3n+6,1. By an “approximate isometric embedding” we mean an embedding which preserves the energy functional on a prescribed set of geodesics connecting a dense set of points.

中文翻译：

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长度度量空间的等距嵌入问题

我们证明了每一个适当的n维长度度量空间允许“近似等距嵌入”到洛伦兹空间ℝ3n+6,1. “近似等距嵌入”是指在连接一组密集点的指定测地线集上保留能量泛函的嵌入。