Isometric embedding of negatively curved complete surfaces in   Lorentz-Minkowski space
  Hilbert-Efimov theorem states that any complete surface with curvature bounded above by a negative constant can not be isometrically imbedded in $\mathbb{R}^3.$ We demonstrate that any simply-connected smooth complete surface with curvature bounded above by a negative constant admits a smooth isometric embedding into the Lorentz-Minkowski space $\mathbb{R}^{2,1}$. 
Bing-Long Chen and Le Yin
math.DG math.AP