The Non-Abelian X-Ray Transform on Asymptotically Hyperbolic Spaces

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dc.contributor.advisorUhlmann, Gunther
dc.contributor.authorGrebnev, Haim
dc.date.accessioned2024-09-09T23:12:42Z
dc.date.available2024-09-09T23:12:42Z
dc.date.issued2024-09-09
dc.date.submitted2024
dc.descriptionThesis (Ph.D.)--University of Washington, 2024
dc.description.abstractWe formulate and prove a gauge equivalence for unitary connections and skew-Hermitian Higgs fields of suitable regularity that are mapped to the same function under the non-abelian X-ray transform on nontrapping asymptotically hyperbolic spaces with negative curvature and no nontrivial twisted conformal Killing tensor fields with certain regularity. If one furthermore fixes such a connection with zero curvature, a corollary provides an injectivity result for the non-abelian X-ray transform over skew-Hermitian Higgs fields.
dc.embargo.termsOpen Access
dc.format.mimetypeapplication/pdf
dc.identifier.otherGrebnev_washington_0250E_26815.pdf
dc.identifier.urihttps://hdl.handle.net/1773/52107
dc.language.isoen_US
dc.rightsCC BY-NC-ND
dc.subjectAsymptotically hyperbolic spaces
dc.subjectNon-Abelian X-ray transform
dc.subjectTransport equation
dc.subjectTwisted conformal Killing tensor fields
dc.subjectMathematics
dc.subjectMedical imaging
dc.subjectPhysics
dc.subject.otherMathematics
dc.titleThe Non-Abelian X-Ray Transform on Asymptotically Hyperbolic Spaces
dc.typeThesis

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