dc.contributor.author | Guillarmou, Colin | |
dc.contributor.author | Paternain, Gabriel P. | |
dc.contributor.author | Salo, Mikko | |
dc.contributor.author | Uhlmann, Gunther | |
dc.date.accessioned | 2016-11-21T11:55:10Z | |
dc.date.available | 2016-11-21T11:55:10Z | |
dc.date.issued | 2016 | |
dc.identifier.citation | Guillarmou, C., Paternain, G. P., Salo, M., & Uhlmann, G. (2016). The X-Ray Transform for Connections in Negative Curvature. <i>Communications in Mathematical Physics</i>, <i>343</i>(1), 83-127. <a href="https://doi.org/10.1007/s00220-015-2510-x" target="_blank">https://doi.org/10.1007/s00220-015-2510-x</a> | |
dc.identifier.other | CONVID_25326888 | |
dc.identifier.other | TUTKAID_67964 | |
dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/51941 | |
dc.description.abstract | We consider integral geometry inverse problems for unitary connections
and skew-Hermitian Higgs fields on manifolds with negative sectional curvature.
The results apply to manifolds in any dimension, with or without boundary, and
also in the presence of trapped geodesics. In the boundary case, we show injectivity
of the attenuated ray transform on tensor fields with values in a Hermitian bundle
(i.e. vector valued case). We also show that a connection and Higgs field on a
Hermitian bundle are determined up to gauge by the knowledge of the parallel
transport between boundary points along all possible geodesics. The main tools are
an energy identity, the Pestov identity with a unitary connection, which is presented
in a general form, and a precise analysis of the singularities of solutions of transport
equations when there are trapped geodesics. In the case of closed manifolds, we
obtain similar results modulo the obstruction given by twisted conformal Killing
tensors, and we also study this obstruction. | |
dc.language.iso | eng | |
dc.publisher | Springer Berlin Heidelberg | |
dc.relation.ispartofseries | Communications in Mathematical Physics | |
dc.subject.other | X-ray transforms | |
dc.subject.other | connections | |
dc.subject.other | Higgs fields | |
dc.subject.other | Hermitian bundles | |
dc.title | The X-Ray Transform for Connections in Negative Curvature | |
dc.type | article | |
dc.identifier.urn | URN:NBN:fi:jyu-201611184675 | |
dc.contributor.laitos | Matematiikan ja tilastotieteen laitos | fi |
dc.contributor.laitos | Department of Mathematics and Statistics | en |
dc.contributor.oppiaine | Matematiikka | fi |
dc.contributor.oppiaine | Mathematics | en |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | |
dc.date.updated | 2016-11-18T13:15:35Z | |
dc.type.coar | journal article | |
dc.description.reviewstatus | peerReviewed | |
dc.format.pagerange | 83-127 | |
dc.relation.issn | 1432-0916 | |
dc.relation.numberinseries | 1 | |
dc.relation.volume | 343 | |
dc.type.version | acceptedVersion | |
dc.rights.copyright | © Springer-Verlag Berlin Heidelberg 2015. This is a final draft version of an article whose final and definitive form has been published by Springer. Published in this repository with the kind permission of the publisher. | |
dc.rights.accesslevel | openAccess | fi |
dc.subject.yso | inversio-ongelmat | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p27912 | |
dc.relation.doi | 10.1007/s00220-015-2510-x | |