Existence of Abelian BPS Vortices on Surfaces with Neumann Boundary Conditions

Abstract Existence of abelian BPS vortices on a manifold with boundary satisfying Neumann boundary conditions is proved. Numerical solutions are constructed on the Euclidean disk, and the $$L^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> -metric of the moduli space of one vortex located at the interior of a rotationally symmetric disk is studied. The results presented extend previous work of Manton and Zhao on quotients of surfaces that admit a reflection.