Magnetic monopoles on manifolds with boundary

Abstract

Kapustin and Witten associate a Hecke modification of a holomorphic bundle over a Riemann surface to a singular monopole on a Riemannian surface times an interval satisfying prescribed boundary conditions. We prove the existence and uniqueness of singular monopoles satisfying prescribed boundary conditions for any given Hecke modification data confirming the underlying geometric invariant theory principle. © 2010 American Mathematical Society.