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PreprintarXiv licencearXiv

The Non-Abelian X-Ray Transform on Simple Asymptotically Hyperbolic Surfaces

  • Nikolas Eptaminitakis
  • Haim Grebnev
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Abstract

We prove a gauge equivalence result for the non-Abelian X-ray transform with connection and Higgs field on simple 2-dimensional asymptotically hyperbolic spaces. Our approach is based on the construction of holomorphic integrating factors. To construct these, we analyze the geodesic X-ray transform on functions on simple asymptotically hyperbolic manifolds of general dimension and prove polyhomogeneous mapping properties and a surjectivity result for the adjoint.

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Cite

BibTeXRIS
BibTeX
@misc{eptaminitakis2026nonabelian,
  title = {{The Non-Abelian X-Ray Transform on Simple Asymptotically Hyperbolic Surfaces}},
  author = {Nikolas Eptaminitakis and Haim Grebnev},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02264},
  eprint = {2611.02264},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.02264},
}
RIS
TY  - UNPB
TI  - The Non-Abelian X-Ray Transform on Simple Asymptotically Hyperbolic Surfaces
AU  - Nikolas Eptaminitakis
AU  - Haim Grebnev
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.02264
UR  - https://arxiv.org/abs/2611.02264
AB  - We prove a gauge equivalence result for the non-Abelian X-ray transform with connection and Higgs field on simple 2-dimensional asymptotically hyperbolic spaces. Our approach is based on the construction of holomorphic integrating factors. To construct these, we analyze the geodesic X-ray transform on functions on simple asymptotically hyperbolic manifolds of general dimension and prove polyhomogeneous mapping properties and a surjectivity result for the adjoint.
ER  -