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 (2)

• 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