A generalization of inversion formulas of Pestov and Uhlmann

TL;DR

This paper extends the inversion formulas for the geodesic ray transform, originally developed by Pestov and Uhlmann, to a broader class of simple 2D manifolds with near-constant curvature.

Contribution

It generalizes existing inversion formulas to simple 2D manifolds with curvatures close to constant, broadening their applicability.

Findings

Inversion formulas now apply to manifolds with near-constant curvature.

The formulas are valid for functions and vector fields on these manifolds.

This extends the scope of geodesic ray transform inversion methods.

Abstract

In this note, we give a generalization of the inversion formulas of Pestov-Uhlmann for the geodesic ray transform of functions and vector fields on simple 2-dimensional manifolds of constant curvature. The inversion formulas given here hold for 2-dimensional simple manifolds whose curvatures close to a constant.