1. Ginzburg–Landau equations on Riemann surfaces of higher genus
- Author
-
Nicholas M. Ercolani, Steven Rayan, D. Chouchkov, and Israel Michael Sigal
- Subjects
Surface (mathematics) ,Holomorphic function ,FOS: Physical sciences ,01 natural sciences ,35Q56, 35Q40, 81Q70, 81V70 ,symbols.namesake ,Mathematics - Analysis of PDEs ,Mathematics::Algebraic Geometry ,Genus (mathematics) ,0103 physical sciences ,FOS: Mathematics ,0101 mathematics ,Mathematical Physics ,Mathematical physics ,Physics ,Degree (graph theory) ,Applied Mathematics ,Riemann surface ,010102 general mathematics ,Mathematical Physics (math-ph) ,Moduli space ,Constant curvature ,Line (geometry) ,symbols ,010307 mathematical physics ,Analysis ,Analysis of PDEs (math.AP) - 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., Comment: 37 pages
- Published
- 2020