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On the isometric embedding problem for length metric spaces

Research paper by Barry Minemyer

Indexed on: 28 Jan '16Published on: 28 Jan '16Published in: Mathematics - Metric Geometry



Abstract

We prove that every proper $n$-dimensional length metric space admits an "approximate isometric embedding" into Lorentzian space $\mathbb{R}^{3n+6,1}$. 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.