On a non-elliptic attenuated geodesic transform

TL;DR

This paper investigates the attenuated geodesic transform on compact Riemannian surfaces with boundary, extending known results by removing the need for the absence of conjugate points, thus broadening the understanding of uniqueness and stability.

Contribution

It generalizes existing results on the attenuated geodesic transform by eliminating the conjugate points condition, enhancing the theoretical framework for inverse problems on Riemannian surfaces.

Findings

Established uniqueness of the transform without conjugate points.

Proved stability results under more general conditions.

Extended the applicability of inverse problem techniques to broader geometric settings.

Abstract

For a compact Riemannian surface with boundary we study attenuated geodesic transform of functions and differential forms. We generalize several known results on uniqueness and stability of this transform dropping condition of absence of conjugate points.