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

Abstract

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