6533b857fe1ef96bd12b46dd
RESEARCH PRODUCT
Geodesic X-ray tomography for piecewise constant functions on nontrapping manifolds
Jere LehtonenJoonas IlmavirtaMikko Salosubject
Mathematics - Differential GeometryGeodesicinverse problemsGeneral Mathematics010102 general mathematicsGeodesic mapMathematical analysisBoundary (topology)16. Peace & justice01 natural sciencesManifoldFoliationinversio-ongelmatDifferential Geometry (math.DG)0103 physical sciencesPiecewiseFOS: Mathematics010307 mathematical physicsConstant functionMathematics::Differential Geometry0101 mathematicsConvex functionMathematics::Symplectic GeometryMathematicsdescription
We show that on a two-dimensional compact nontrapping manifold with strictly convex boundary, a piecewise constant function is determined by its integrals over geodesics. In higher dimensions, we obtain a similar result if the manifold satisfies a foliation condition. These theorems are based on iterating a local uniqueness result. Our proofs are elementary.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-02-24 |