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

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