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The boundary rigidity problem consists in determining a compact, Riemannian manifold with boundary, up to isometry, by knowing the boundary distance function between boundary points. In this paper we announce the result of our forthcoming article that one can solve this problem for generic simple metrics. Moreover we probe stability estimates for this problem.

Copyright 2005 American Mathematical Society
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Article Info

• ERA Amer. Math. Soc. 11 (2005), pp. 64-70
• Publisher Identifier: S 1079-6762(05)00148-4
• 2000 Mathematics Subject Classification. Primary 53C20
• Key words and phrases. Boundary rigidity, Riemannian manifold, inverse problem
• Received by editors March 8, 2005
• Posted on June 23, 2005
• Communicated by Dmitri Burago
• Comments (When Available)

Plamen Stefanov

Department of Mathematics, Purdue University, West Lafayette, IN 47907

E-mail address: stefanov@math.purdue.edu

Gunther Uhlmann

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

E-mail address: gunther@math.washington.edu

The first author was supported in part by NSF Grant DMS-0400869.
The second author was supported in part by NSF Grant DMS-0245414.