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Two Dimensional Compact Simple Riemannian Manifolds Are Boundary Distance Rigid

Leonid Pestov and Gunther Uhlmann
Annals of Mathematics
Second Series, Vol. 161, No. 2 (Mar., 2005), pp. 1093-1110
Published by: Annals of Mathematics
Stable URL: http://www.jstor.org/stable/3597325
Page Count: 18
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Two Dimensional Compact Simple Riemannian Manifolds Are Boundary Distance Rigid
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Abstract

We prove that knowing the lengths of geodesics joining points of 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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