6533b7dafe1ef96bd126ecd7
RESEARCH PRODUCT
Pestov identities and X-ray tomography on manifolds of low regularity
Joonas IlmavirtaAntti Kykkänensubject
Mathematics - Differential Geometrynon-smooth geometrygeodesic X-ray tomographyinverse problems44A12 53C22 53C65 58J32Pestov identityinversio-ongelmatdifferentiaaligeometriaRiemannin monistotMathematics - Analysis of PDEsDifferential Geometry (math.DG)tomografiaintegraalilaskentaFOS: MathematicsMathematics::Differential Geometryintegral geometryAnalysis of PDEs (math.AP)description
We prove that the geodesic X-ray transform is injective on scalar functions and (solenoidally) on one-forms on simple Riemannian manifolds $(M,g)$ with $g \in C^{1,1}$. In addition to a proof, we produce a redefinition of simplicity that is compatible with rough geometry. This $C^{1,1}$-regularity is optimal on the H\"older scale. The bulk of the article is devoted to setting up a calculus of differential and curvature operators on the unit sphere bundle atop this non-smooth structure.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-12-10 |