Michel's conjecture on boundary rigidity of simple manifolds

A compact Riemannian manifold with boundary is simple when it has strictly convex boundary, every two points are connected by a unique geodesic segment, and it has no conjugate points. It is boundary rigid when its metric is uniquely determined by its boundary distance function: any compact Riemannian manifold with the same boundary and boundary distance function is isometric to it via a boundary-preserving isometry.

Michel's conjecture. All simple manifolds are boundary rigid.

The conjecture asserts global uniqueness of a metric from boundary distance data in the simple-manifold setting. Its resolution status is not specified in the supplied source context.