Thurston's conjecture on convex hyperbolic metrics with prescribed boundary metric

Let $M$ be a 3-dimensional manifold with boundary which admits a complete, convex co-compact metric. For a smooth metric $h$ on $\partial M$ with curvature $K>-1$, the boundary metric is prescribed as follows: the hyperbolic metric on $M$ must induce $h$ on $\partial M$.

Thurston's conjecture. There is a unique hyperbolic metric $g$ on $M$ which induces $h$ on the boundary, and for which the boundary is convex.

This conjecture generalizes the boundary-value problem for hyperbolic metrics on the 3-dimensional ball to other 3-manifolds with boundary. The supplied text does not state whether it has been resolved.