Local X-ray Transform on Asymptotically Hyperbolic Manifolds via Projective Compactification

TL;DR

This paper proves local injectivity of the geodesic X-ray transform near a boundary point on asymptotically hyperbolic manifolds, even with certain metric perturbations, in dimensions three and higher.

Contribution

It establishes local injectivity results for the geodesic X-ray transform on asymptotically hyperbolic manifolds with specific metric regularity.

Findings

Proves local injectivity near boundary points

Handles metrics with even mod $O( ho^5)$ regularity

Applicable in dimensions three and higher

Abstract

We prove local injectivity near a boundary point for the geodesic X-ray transform for an asymptotically hyperbolic metric even mod $O(\rho^5)$ in dimensions three and higher.