Tomography of 1-forms on a gas giant

TL;DR

This paper demonstrates that on gas giant manifolds, the geodesic X-ray transform is solenoidally injective for smooth one-forms, using Pestov identities and asymptotic analysis of geodesics.

Contribution

It establishes the solenoidal injectivity of the geodesic X-ray transform on a new class of manifolds called gas giant manifolds, expanding understanding of inverse problems in geometric analysis.

Findings

Injectivity holds for smooth one-forms on gas giant manifolds.

Proof utilizes Pestov identity and asymptotic analysis.

Gas giant manifolds have milder boundary singularities than asymptotically hyperbolic spaces.

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.