by Joonas Ilmavirta, Antti Kykkänen and Eetu Satukangas
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.
Reference:
Tomography of 1-forms on a gas giant (Joonas Ilmavirta, Antti Kykkänen and Eetu Satukangas), 2026.
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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.
[arXiv]
Bibtex Entry:
@unpublished{gg-1-form,
author = {Joonas Ilmavirta and Antti Kykk\"{a}nen and Eetu Satukangas},
title = {{Tomography of 1-forms on a gas giant}},
month = feb,
year = 2026,
arxiv = {2602.10322},
url = {http://users.jyu.fi/~jojapeil/pub/gg-1-form.pdf},
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.},
gsid = {9099575586141042345}
}