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.
References
Primary source
Yuping Ruan, “Filling volume minimality and boundary rigidity of metrics close to a negatively curved symmetric metric”, arXiv:2201.09175 (2022).
Additional references
5 papers in this index state this conjecture (2010–2022). The statement above is taken from the most recent of them; the others are arXiv:2107.05119, arXiv:1405.1712, arXiv:1011.1570, arXiv:1004.2505.
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