2 citations · 5 across the 10 of their papers we have counts for
10 papers
A family of non-simple surfaces whose transport twistor spaces admit global blow-down maps
François Monard, Zhengyi Qi
In the literature on X-ray transform and Transport Twistor (TT) spaces, blow-down maps (or maps with holomorphic blow-down structure as defined in [BMP24]) are maps that desingular…
The hyperbolic X-ray transform: new range characterizations, mapping properties and functional relations
Nikolas Eptaminitakis, François Monard, Yuzhou Zou
We derive new singular value decompositions and range characterizations for the X-ray transform on the Poincaré disk, intertwining relations with distinguished differential operato…
Local and Global Blow Downs of Transport Twistor Space
Jan Bohr, François Monard, Gabriel P. Paternain
Transport twistor spaces are degenerate complex -dimensional manifolds that complexify transport problems on Riemannian surfaces, appearing, e.g., in geometric inverse probl…
Non-standard Sobolev scales and the mapping properties of the X-ray transform on manifolds with strictly convex boundary
François Monard
This article surveys recent results aiming at obtaining refined mapping estimates for the X-ray transform on a Riemannian manifold with boundary, which leverage the condition that…
Boundary triples for a family of degenerate elliptic operators of Keldysh type
François Monard, Yuzhou Zou
We consider a one-parameter family of degenerately elliptic operators on the closed disk , of Keldysh (or Kimura) type, which appears in prior work [Mishra…
Range characterizations and Singular Value Decomposition of the geodesic X-ray transform on disks of constant curvature
Rohit Kumar Mishra, François Monard
For a one-parameter family of simple metrics of constant curvature ( for ) on the unit disk , we first make explicit the Pestov-Uhlmann range characterization o…
On solenoidal-injective and injective ray transforms of tensor fields on surfaces
Venkateswaran P. Krishnan, Rohit Kumar Mishra, François Monard
We first give a constructive answer to the attenuated tensor tomography problem on simple surfaces. We then use this result to propose two approaches to produce vector-valued integ…
Integral geometry on manifolds with boundary and applications
Joonas Ilmavirta, François Monard
We survey recent results on inverse problems for geodesic X-ray transforms and other linear and non-linear geometric inverse problems for Riemannian metrics, connections and Higgs…
Efficient tensor tomography in fan-beam coordinates. II: Attenuated transforms
François Monard
This article extends the author's past work [Inv. Probl. Imaging, 10:2 (2016), 433--459] to attenuated X-ray transforms, where the attenuation is complex-valued and only depends on…
Reconstruction formulas for X-ray transforms in negative curvature
Colin Guillarmou, François Monard
We give reconstruction formulas inverting the geodesic X-ray transform over functions (call it ) and solenoidal vector fields on surfaces with negative curvature and strictly…