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arXiv · 1602.02946

Marked boundary rigidity for surfaces

Colin Guillarmou·Marco Mazzucchelli
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Abstract

We show that, on an oriented compact surface, two sufficiently $C^2$-close Riemannian metrics with strictly convex boundary, no conjugate points, hyperbolic trapped set for their geodesic flows, and same marked boundary distance, are isometric via a diffeomorphism that fixes the boundary. We also prove that the same conclusion holds on a compact surface for any two negatively curved Riemannian metrics with strictly convex boundary and same marked boundary distance, extending a result of Croke and Otal.

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Colin Guillarmou, Marco Mazzucchelli. 2016-02-09. Marked boundary rigidity for surfaces. https://doi.org/10.1017/etds.2016.94

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