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 ${\mathbb{R}}^3\mathrm{.}$ 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 ${\mathbb{R}}^{2,1}$.