activity
20192026
most citedLocal X-ray Transform on Asymptotically Hyperbolic Manifolds via Projective Compactification

5 citations · 8 across the 9 of their papers we have counts for

collaborators

10 papers

math.DG2026

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)…

math.DG2025

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…

math.AP2025

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…

math.AP2024

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…

math.DG2023

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…

math.AP2022

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…

math.AP2021

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…

math.DG2021★ 5 cited

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.

math.AP2021★ 3 cited

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…

math.DG2019

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.