  We prove that any metric with curvature $\leq -1$ (in the sense of A. D.
Alexandrov) on a closed surface of genus $>1$ is isometric to the induced
intrinsic metric on a space-like convex surface in a Lorentzian manifold of
dimension $(2+1)$ with sectional curvature $-1$. The proof is done by
approximation, using a result about isometric immersion of smooth metrics by
Labourie--Schlenker.
