  A compact Fuchsian manifold with boundary is a hyperbolic 3-manifold
homeomorphic to $S_g \times [0; 1]$ such that the boundary component $S_g
\times \{ 0\}$ is geodesic. We prove that a compact Fuchsian manifold with
convex boundary is uniquely determined by the induced path metric on $S_g
\times \{1\}$. We do not put further restrictions on the boundary except
convexity.
