On Calderon's problem for the connection Laplacian

TL;DR

This paper addresses Calderon's inverse problem for the connection Laplacian on real-analytic vector bundles, proving uniqueness in recovering geometric and topological data from boundary measurements.

Contribution

It establishes a uniqueness theorem for the connection Laplacian, recovering bundle topology and geometry under real-analytic assumptions, up to gauge and isometry.

Findings

Unique recovery of vector bundle topology and geometry

Recovery up to gauge transformation and isometry

Applicability to real-analytic geometric data

Abstract

We consider Calderon's problem for the connection Laplacian on a real-analytic vector bundle over a manifold with boundary. We prove a uniqueness result for this problem when all geometric data are real-analytic, recovering the topology and geometry of a vector bundle up to a gauge transformation and an isometry of the base manifold.