Ginzburg-Landau equations on Riemann surfaces of higher genus

Abstract

We study the Ginzburg-Landau equations on Riemann surfaces of arbitrary genus. In particular: - we construct explicitly the (local moduli space of gauge-equivalent) solutions in a neighbourhood of the constant curvature ones; - classify holomorphic structures on line bundles arising as solutions to the equations in terms of the degree, the Abel-Jacobi map, and symmetric products of the surface; - determine the form of the energy and identify when it is below the energy of the constant curvature (normal) solutions.

37 pages

References in corpus (2)

• On the L^2-metric of vortex moduli spaces
• On Abrikosov Lattice Solutions of the Ginzburg-Landau Equations

Cited by in corpus (4)

• Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in a Weak Homogeneous Magnetic Field
• Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in General External Fields
• Ginzburg-Landau Equations on Non-compact Riemann Surfaces
• On the bifurcation theory of the Ginzburg-Landau equations