Interaction energy between vortices of vector fields on Riemannian surfaces

Abstract

We study a variational Ginzburg–Landau-type model depending on a small parameter ε>0 for (tangent) vector fields on a 2-dimensional Riemannian surface. As ε→0, the vector fields tend to be of unit length and will have singular points of a (non-zero) index, called vortices. Our main result determines the interaction energy between these vortices as a Γ-limit (at the second order) as ε→0.