Convex-core metric rigidity conjecture for geometrically finite hyperbolic 3-manifolds

Let $M$ be a geometrically finite hyperbolic 3-manifold, meaning that its convex core has finite volume. Its convex core is the intersection of all closed totally convex subsets of $M$, where a subset is totally convex if it contains every geodesic segment joining any two of its points. Convex-core metric rigidity conjecture. The geometry of $M$ is completely determined by its topology and the induced path metric on the boundary of its convex core. This is described as a long-standing conjecture and would provide an alternative to determining the geometry from the conformal structure at infinity.