4 papers
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 operat…
Scattering rigidity for Hamiltonian systems with an application to Finsler geometry
Nikolas Eptaminitakis, Plamen Stefanov
We study scattering rigidity for Hamiltonian systems on , where is a manifold with boundary equipped with a positively homogeneous Hamiltonian function $H(x,ξ…
Tensor Tomography on Asymptotically Hyperbolic Surfaces
Nikolas Eptaminitakis, François Monard, François Monard +1
We initiate a study of the inversion of the geodesic X-ray transform over symmetric -tensor fields on asymptotically hyperbolic surfaces. This operator has a non-trivial k…
The DC Kerr Effect in Nonlinear Optics
Nikolas Eptaminitakis, Plamen Stefanov
We use weakly nonlinear geometric optics to study a model for the DC Kerr effect (the Kerr electro-optic effect), in which a light beam propagating through a material with strong n…