Local X-ray transform on asymptotically hyperbolic manifolds via projective compactification

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Nikolas Eptaminitakis
  • C. Robin Graham

Externe Organisationen

  • Purdue University
  • University of Washington
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)733-763
Seitenumfang31
FachzeitschriftNew Zealand Journal of Mathematics
Jahrgang52
PublikationsstatusVeröffentlicht - 14 Dez. 2021
Extern publiziertJa

Abstract

We prove local injectivity near a boundary point for the geodesic X-ray transform for an asymptotically hyperbolic metric even mod O(ρ5) in dimensions three and higher.

ASJC Scopus Sachgebiete

Zitieren

Local X-ray transform on asymptotically hyperbolic manifolds via projective compactification. / Eptaminitakis, Nikolas; Graham, C. Robin.
in: New Zealand Journal of Mathematics, Jahrgang 52, 14.12.2021, S. 733-763.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Eptaminitakis, N & Graham, CR 2021, 'Local X-ray transform on asymptotically hyperbolic manifolds via projective compactification', New Zealand Journal of Mathematics, Jg. 52, S. 733-763. https://doi.org/10.53733/191
Eptaminitakis, N., & Graham, C. R. (2021). Local X-ray transform on asymptotically hyperbolic manifolds via projective compactification. New Zealand Journal of Mathematics, 52, 733-763. https://doi.org/10.53733/191
Eptaminitakis N, Graham CR. Local X-ray transform on asymptotically hyperbolic manifolds via projective compactification. New Zealand Journal of Mathematics. 2021 Dez 14;52:733-763. doi: 10.53733/191
Eptaminitakis, Nikolas ; Graham, C. Robin. / Local X-ray transform on asymptotically hyperbolic manifolds via projective compactification. in: New Zealand Journal of Mathematics. 2021 ; Jahrgang 52. S. 733-763.
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note = "Funding Information: Then (6.24) for k = 1 follows exactly the same steps as for k = 0 from (6.25) onwards, with KE replaced( by W) j KE − ((Wj h)/h)KE: by Lemma 6.7, Wj KE − ((Wj h)/h)KE ∈ C0 Od2 × [0, η0) , it vanishes to infinite order at Gb × [0, η0) and is identically 0 for η = 0. This finishes the proof of the proposition. □ Acknowledgments. Research of N.E. was partially supported by the National Science Foundation under Grant No. DMS-1800453 of Gunther Uhlmann. The authors would like to thank Hart Smith, Gunther Uhlmann, and Andr{\'a}s Vasy for helpful discussions. This paper is based on Chapter 1 of N.E.{\textquoteright}s University of Washington PhD Thesis ([Ept20]). ",
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