Work

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

Year: 2026

Type: article

Abstract: In this paper we 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.

Source: Journal of Geometric Analysis

DOI: 10.1007/s12220-025-02296-7

Author: Haim Grebnev

Institution: Purdue University West Lafayette

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: National Science Foundation