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## Recent progress on the boundary rigidity problem

### Plamen Stefanov and Gunther Uhlmann

**Abstract.**
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.

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