Partial data inverse problems for magnetic Schr\"odinger operators on conformally transversally anisotropic manifolds

TL;DR

This paper proves a global uniqueness result for inverse boundary problems involving magnetic Schrödinger operators on certain manifolds, using partial boundary data and the injectivity of the geodesic X-ray transform.

Contribution

It establishes the first global uniqueness result for magnetic and electric potentials on conformally transversally anisotropic manifolds with partial boundary data.

Findings

Uniqueness of magnetic and electric potentials from partial boundary measurements

Extension of inverse boundary problem results to less regular potentials

Application of geodesic X-ray transform injectivity in inverse problems

Abstract

We study inverse boundary problems for the magnetic Schr\"odinger operator with H\"older continuous magnetic potentials and continuous electric potentials on a conformally transversally anisotropic Riemannian manifold of dimension n greater than or equal to three with connected boundary. A global uniqueness result is established for magnetic fields and electric potentials from the partial Cauchy data on the boundary of the manifold provided that the geodesic X-ray transform on the transversal manifold is injective.