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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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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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