Ginzburg–Landau equations on Riemann surfaces of higher genus

D. Chouchkov, N. M. Ercolani, S. Rayan, I. M. Sigal

Research output: Contribution to journalArticle

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 the neighborhood 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.

Original languageEnglish (US)
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
DOIs
StateAccepted/In press - Jan 1 2019

Keywords

  • Elliptic equations on Riemann surfaces
  • Ginzburg–Landau equations
  • Holomorphic bundles
  • Superconductivity
  • Vortex lattices
  • Vortices

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

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