Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0992.35120
Lassas, Matti; Uhlmann, Gunther
On determining a Riemannian manifold from the Dirichlet-to-Neumann map. (English)
[J] Ann. Sci. Éc. Norm. Supér. (4) 34, No. 5, 771-787 (2001). ISSN 0012-9593

Summary: We study the inverse problem of determining a Riemannian manifold from the boundary data of harmonic functions. This problem arises in electrical impedance tomography, where one tries to find an unknown conductivity inside a given body from voltage and current measurements made at the boundary of the body. We show that one can reconstruct the conformal class of a smooth, compact Riemannian surface with boundary from the set of Cauchy data, given on a non-empty open subset of the boundary, of all harmonic functions. Also, we show that one can reconstruct in dimension $n\ge 3$ compact real-analytic manifolds with boundary from the same information. We make no assumptions on the topology of the manifold other than connectedness.

MSC 2000:: *35R30 Inverse problems for PDE
58J32 Boundary value problems on manifolds
31C12 Potential theory on Riemannian manifolds
35J05 Laplace equation, etc.

Keywords: electrical impedance tomography; compact Riemannian surface; Cauchy data; harmonic functions

Cited in: Zbl 1229.58024 Zbl 1227.35245 Zbl 1118.32009 Zbl 1197.58008 Zbl 1048.58019

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Article Journal Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]