Identification of a connection from Cauchy data on a Riemann surface with boundary

Abstract

We consider a connection ${\nabla }^X$ on a complex line bundle over a Riemann surface with boundary $M_0$, with connection 1-form $X$. We show that the Cauchy data space of the connection Laplacian (also called magnetic Laplacian) $L:={{\nabla }^X}^{\ast }{\nabla }^X+q$, with $q$ a complex valued potential, uniquely determines the connection up to gauge isomorphism, and the potential $q$.

23 pages. Independent additional proof of Th 6.1 added. Minor typos corrected

References in corpus (4)

• Calderon inverse Problem with partial data on Riemann Surfaces
• Global uniqueness from partial Cauchy data in two dimensions
• On the reconstruction of conductivity of bordered two-dimensional surface in R^3 from electrical currents measurements on its boundary
• Gauge Equivalence and Inverse Scattering for Aharonov-Bohm Effect

Cited by in corpus (6)

• The Calderon problem with partial data on manifolds and applications
• Inverse problems for magnetic Schrödinger operators in transversally anisotropic geometries
• Partial Data Inverse Problems for Nonlinear Magnetic Schrödinger Equations
• An Inverse Problem for Non-linear Fractional Magnetic Schrodinger Equation
• Rough Potential Recovery in the Plane
• A note on the partial data inverse problem for a nonlinear magnetic Schrödinger operator on Riemann surface