Tomography of 1-forms on a gas giant
Differential Geometry
2026-02-12 v1
Abstract
We show that on gas giant manifolds the geodesic X-ray transform is solenoidally injective on one-forms that are smooth up to the boundary in an appropriate smooth structure. A gas giant manifold is a conformally blown up Riemannian manifold whose boundary singularity is milder than asymptotically hyperbolic. The proof is based on a Pestov identity and asymptotic analysis of short geodesics.
Keywords
Cite
@article{arxiv.2602.10322,
title = {Tomography of 1-forms on a gas giant},
author = {Joonas Ilmavirta and Antti Kykkänen and Eetu Satukangas},
journal= {arXiv preprint arXiv:2602.10322},
year = {2026}
}
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29 pages