X-ray Transform and Boundary Rigidity for Asymptotically Hyperbolic Manifolds

TL;DR

This paper investigates the boundary rigidity problem for asymptotically hyperbolic manifolds, demonstrating injectivity of the X-ray transform and addressing the nonlinear inverse problem of recovering metrics from boundary data.

Contribution

It establishes injectivity results for the X-ray transform and advances understanding of metric recovery from boundary measurements in asymptotically hyperbolic manifolds.

Findings

Injectivity of the X-ray transform in several cases

Results on recovering metrics from boundary measurements

Progress on the nonlinear inverse problem

Abstract

We consider the boundary rigidity problem for asymptotically hyperbolic manifolds. We show injectivity of the X-ray transform in several cases and consider the non-linear inverse problem which consists of recovering a metric from boundary measurements for the geodesic flow.