On the isometric embedding problem for length metric spaces
  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. 
Barry Minemyer
math.MG math-ph math.DG math.MP