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dc.contributor.authorPaternain, Gabriel
dc.contributor.authorSalo, M
dc.contributor.authorUhlmann, G
dc.contributor.authorZhou, Hanming
dc.date.accessioned2018-09-20T09:32:44Z
dc.date.available2018-09-20T09:32:44Z
dc.date.issued2019-12
dc.identifier.issn0002-9327
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/280373
dc.description.abstractConsider a compact Riemannian manifold of dimension $\geq 3$ with strictly convex boundary, such that the manifold admits a strictly convex function. We show that the attenuated ray transform in the presence of an arbitrary connection and Higgs field is injective modulo the natural obstruction for functions and one-forms. We also show that the connection and the Higgs field are uniquely determined by the scattering relation modulo gauge transformations. The proofs involve a reduction to a local result showing that the geodesic X-ray transform with a matrix weight can be inverted locally near a point of strict convexity at the boundary, and a detailed analysis of layer stripping arguments based on strictly convex exhaustion functions. As a somewhat striking corollary, we show that these integral geometry problems can be solved on strictly convex manifolds of dimension $\geq 3$ having non-negative sectional curvature (similar results were known earlier in negative sectional curvature). We also apply our methods to solve some inverse problems in quantum state tomography and polarization tomography.
dc.publisherProject Muse
dc.titleThe geodesic X-ray transform with matrix weights
dc.typeArticle
prism.endingPage1750
prism.issueIdentifier6
prism.publicationDate2019
prism.publicationNameAmerican Journal of Mathematics
prism.startingPage1707
prism.volume141
dc.identifier.doi10.17863/CAM.27744
dcterms.dateAccepted2018-04-18
rioxxterms.versionofrecord10.1353/ajm.2019.0045
rioxxterms.versionAM
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserved
rioxxterms.licenseref.startdate2019-12-01
dc.contributor.orcidZhou, Hanming [0000-0002-2188-4445]
dc.identifier.eissn1080-6377
rioxxterms.typeJournal Article/Review
pubs.funder-project-idEngineering and Physical Sciences Research Council (EP/M023842/1)
rioxxterms.freetoread.startdate2019-09-26


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