The reflection principle and Calder\'on problems with partial data

TL;DR

This paper addresses the Calderón inverse problem on Riemann surfaces, demonstrating how to recover connections from partial boundary data, advancing understanding in geometric inverse problems.

Contribution

It solves the partial data Calderón problem for the connection Laplacian specifically on Riemann surfaces, a novel extension in inverse boundary value problems.

Findings

Successfully reconstructs connections from partial boundary measurements.

Extends Calderón problem solutions to Riemann surfaces.

Provides new methods for inverse problems with partial data.

Abstract

We solve the partial data Calder\'on problem for the connection Laplacian on Riemann surfaces.