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dc.contributor.authorPaternain, Gabriel P.
dc.contributor.authorSalo, Mikko
dc.contributor.authorUhlmann, Gunther
dc.date.accessioned2015-01-12T09:22:33Z
dc.date.available2015-01-12T09:22:33Z
dc.date.issued2014
dc.identifier.citationPaternain, G., Salo, M., & Uhlmann, G. (2014). Spectral rigidity and invariant distributions on Anosov surfaces. <em>Journal of differential geometry</em>, 98 (1), 147-181. Retrieved from <a href="http://projecteuclid.org/euclid.jdg/1406137697">http://projecteuclid.org/euclid.jdg/1406137697</a>
dc.identifier.otherTUTKAID_62681
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/45053
dc.description.abstractThis article considers inverse problems on closed Riemannian surfaces whose geodesic flow is Anosov. We prove spectral rigidity for any Anosov surface and injectivity of the geodesic ray transform on solenoidal 2-tensors. We also establish surjectivity results for the adjoint of the geodesic ray transform on solenoidal tensors. The surjectivity results are of independent interest and imply the existence of many geometric invariant distributions on the unit sphere bundle. In particular, we show that on any Anosov surface (M,g), given a smooth function f on M there is a distribution in the Sobolev space H-1(SM) that is invariant under the geodesic flow and whose projection to M is the given function f.
dc.language.isoeng
dc.publisherLehigh University
dc.relation.ispartofseriesJournal of Differential Geometry
dc.relation.isversionofJournal of differential geometry
dc.relation.urihttp://projecteuclid.org/euclid.jdg/1406137697
dc.subject.otherconjugate-pointsen
dc.subject.otherisospectral manifoldsen
dc.titleSpectral rigidity and invariant distributions on Anosov surfaces
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201501091064
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineMatematiikka
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.date.updated2015-01-09T16:30:10Z
dc.type.coarjournal article
dc.description.reviewstatuspeerReviewed
dc.format.pagerange147-181
dc.relation.issn0022-040X
dc.relation.numberinseries1
dc.relation.volume98
dc.type.versionacceptedVersion
dc.rights.copyright© The Authors. © Lehigh University, 2014. This is an authors' final draft version of an article whose final and definitive form has been published by Lehigh University. Published in this repository with the kind permission of the publisher.
dc.rights.accesslevelopenAccessfi


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