Mathematical Research Letters

Volume 5 (1998)

Number 1

Rigidity for metrics with the same lengths of geodesics

Pages: 83 – 96



Plamen Stefanov (Bulgarian Academy of Sciences)

Gunther Uhlmann (University of Washington, Seattle)


We prove that we can recover a Riemannian metric in a bounded smooth domain in $\Bbb{R}^3$ up to an isometry which is the identity on the boundary, by knowing the lengths of the geodesics joining points on the boundary. We assume that the metrics are close to the euclidian metric $e$.

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