Mathematical Research Letters

Volume 5, Issue 1, January 1998 pp. 83-96.

Rigidity for metrics with the same lengths of geodesics

Authors: Plamen Stefanov, and Gunther Uhlmann
Author institution: Bulgarian Academy of Sciences, and University of Washington, Seattle

Summary: 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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