dc.contributor.author Paternain, Gabriel dc.contributor.author Salo, M dc.contributor.author Uhlmann, G dc.contributor.author Zhou, Hanming dc.date.accessioned 2018-09-20T09:32:44Z dc.date.available 2018-09-20T09:32:44Z dc.date.issued 2019-12 dc.identifier.issn 0002-9327 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/280373 dc.description.abstract Consider 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.publisher Project Muse dc.title The geodesic X-ray transform with matrix weights dc.type Article prism.endingPage 1750 prism.issueIdentifier 6 prism.publicationDate 2019 prism.publicationName American Journal of Mathematics prism.startingPage 1707 prism.volume 141 dc.identifier.doi 10.17863/CAM.27744 dcterms.dateAccepted 2018-04-18 rioxxterms.versionofrecord 10.1353/ajm.2019.0045 rioxxterms.version AM rioxxterms.licenseref.uri http://www.rioxx.net/licenses/all-rights-reserved rioxxterms.licenseref.startdate 2019-12-01 dc.contributor.orcid Zhou, Hanming [0000-0002-2188-4445] dc.identifier.eissn 1080-6377 rioxxterms.type Journal Article/Review pubs.funder-project-id Engineering and Physical Sciences Research Council (EP/M023842/1) rioxxterms.freetoread.startdate 2019-09-26
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