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Two dimensional compact simple Riemannian manifolds are boundary distance rigid

L. Pestov·G. Uhlmann
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Abstract

We prove that knowing the length of geodesics joining points on the boundary of a two-dimensional, compact, simple Riemannian manifold with boundary, we can determine uniquely the Riemannian metric up to the natural obstruction.

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L. Pestov, G. Uhlmann. 2003-05-19. Two dimensional compact simple Riemannian manifolds are boundary distance rigid. https://arxiv.org/abs/math/0305280

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