RECONSTRUCTION OF A COMPACT MANIFOLD FROM THE SCATTERING DATA OF INTERNAL SOURCES

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http://hdl.handle.net/10138/326772

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Lassas , M , Saksala , T & Zhou , H 2018 , ' RECONSTRUCTION OF A COMPACT MANIFOLD FROM THE SCATTERING DATA OF INTERNAL SOURCES ' , Inverse problems and imaging , vol. 12 , no. 4 , pp. 993-1031 . https://doi.org/10.3934/ipi.2018042

Title: RECONSTRUCTION OF A COMPACT MANIFOLD FROM THE SCATTERING DATA OF INTERNAL SOURCES
Author: Lassas, Matti; Saksala, Teemu; Zhou, Hanming
Contributor: University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Department of Mathematics and Statistics
Date: 2018-08
Language: eng
Number of pages: 39
Belongs to series: Inverse problems and imaging
ISSN: 1930-8337
URI: http://hdl.handle.net/10138/326772
Abstract: Given a smooth non-trapping compact manifold with strictly convex boundary, we consider an inverse problem of reconstructing the manifold from the scattering data initiated from internal sources. These data consist of the exit directions of geodesics that are emaneted from interior points of the manifold. We show that under certain generic assumption of the metric, the scattering data measured on the boundary determine the Riemannian manifold up to isometry.
Subject: Inverse problem
Riemannian geometry
geodesics
partial differential equations
compact manifold with boundary
DIFFRACTION TRAVEL-TIMES
RIEMANNIAN MANIFOLD
INVERSE PROBLEMS
WAVE-EQUATION
RIGIDITY
METRICS
111 Mathematics
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