Ginzburg–Landau equations on Riemann surfaces of higher genus

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

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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)
Pages (from-to)79-103
Number of pages25
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume37
Issue number1
DOIs
StatePublished - Jan 1 2020

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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