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T1  - Determination of a Riemannian manifold from the distance difference functions 
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UR  - http://hdl.handle.net/10138/326781 
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A1  - Lassas, Matti; Saksala, Teemu 
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PB  -  
Y1  - 2019 
LA  - eng 
AB  - Let (N, g) be a Riemannian manifold with the distance function d(x, y) and an open subset M subset of N. For x is an element of M we denote by D-x the distance difference function D-x:F x F -> R, given by D-x(z(1), z(2)) = d(x, z(1)) - d(x, z(2)), z(1), z(2) is an element of F = N \ M. We consider the inverse problem of determining the topological and the differentiable structure of the manifold M and the metric g vertical bar M on it when we are given the distance difference data, that is, the ... 
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KW  - Inverse problems; distance functions; embeddings of manifolds; wave equation; INVERSE PROBLEM; PHOTOACOUSTIC TOMOGRAPHY; WAVE-EQUATION; ALGORITHM; RECONSTRUCTION; INTEGRABILITY; EQUIVALENCE; SCATTERING; RECOVERY; INDEX; 111 Mathematics 
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