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Inverse boundary value problems in the horosphere  A link between hyperbolic geometry and electrical impedance tomography
Stability of boundary distance representation and reconstruction of Riemannian manifolds
1.  Department of Mathematics, Okayama University, Tsushimanaka, Okayama, 7008530, Japan 
2.  Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, United Kingdom 
3.  Department of Mathematics, Helsinki University of Technology, P.O. Box 1100, 02015 TKK, Finland 
In applications, the boundary distance representation appears in many inverse problems, where measurements are made on the boundary of the object under investigation. As an example, for the heat equation with an unknown heat conductivity the boundary measurements determine the boundary distance representation of the Riemannian metric which corresponds to this conductivity.
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