Two dimensional compact simple Riemannian manifolds are boundary distance rigid

Leonid Pestov; Gunther Uhlmann

doi:https://doi.org/10.4007/annals.2005.161.1093

Pages 1093-1110 from Volume 161 (2005), Issue 2 by Leonid Pestov, Gunther Uhlmann

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.

Mathematical Subject Classification

Primary 2000: 35R30, 53C60

Milestones

Received: 1 May 2003
Accepted: 20 April 2004
Published online: 1 March 2009

Authors

Leonid Pestov

UGRA Research Institute of Information Technologies, Hanty-Mansiysk 628011, Russian Federation

Gunther Uhlmann

Department of Mathematics, University of Washington, Seattle, WA 98195, United States