Integral geometry on manifolds with boundary and applications

TL;DR

This paper surveys recent advances in inverse problems related to geodesic X-ray transforms and geometric inverse problems on manifolds with boundary, focusing on Riemannian metrics, connections, and Higgs fields.

Contribution

It provides a comprehensive overview of recent results in integral geometry and inverse problems on manifolds with boundary, highlighting new theoretical developments.

Findings

Summary of recent inverse problem solutions

Advances in geodesic X-ray transform analysis

Applications to Riemannian metrics and Higgs fields

Abstract

We survey recent results on inverse problems for geodesic X-ray transforms and other linear and non-linear geometric inverse problems for Riemannian metrics, connections and Higgs fields defined on manifolds with boundary.