5 citations · 8 across the 9 of their papers we have counts for
10 papers
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, Yuzhou Joey Zou
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…
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…
The covariance metric in the Blaschke locus
Xian Dai, Nikolas Eptaminitakis
We prove that the Blaschke locus has the structure of a finite dimensional smooth manifold away from the Teichm{ü}ller space and study its Riemannian manifold structure with respec…
Weakly nonlinear geometric optics for the Westervelt equation and recovery of the nonlinearity
Nikolas Eptaminitakis, Plamen Stefanov
We study the non-diffusive Westervelt equation in the weakly nonlinear regime. We show that the leading profile equation is of Burgers' type. We show that a compactly supported non…
The solid-fluid transmission problem
Nikolas Eptaminitakis, Plamen Stefanov
We study microlocally the transmission problem at the interface between an isotropic linear elastic solid and a linear inviscid fluid. We set up a system of evolution equations des…
Local X-ray Transform on Asymptotically Hyperbolic Manifolds via Projective Compactification
Nikolas Eptaminitakis, C. Robin Graham
We prove local injectivity near a boundary point for the geodesic X-ray transform for an asymptotically hyperbolic metric even mod in dimensions three and higher.
Stability Estimates for the X-Ray Transform on Simple Asymptotically Hyperbolic Manifolds
Nikolas Eptaminitakis
We study the normal operator to the geodesic X-ray transform on functions in the setting of simple asymptotically hyperbolic manifolds. We construct a parametrix for the normal ope…
Asymptotically Hyperbolic Manifolds with Boundary Conjugate Points but no Interior Conjugate Points
Nikolas Eptaminitakis, C. Robin Graham
We construct non-trapping asymptotically hyperbolic manifolds with boundary conjugate points but no interior conjugate points.