Ginzburg–Landau equations on Riemann surfaces of higher genus

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

doi:10.1016/j.anihpc.2019.04.002

Ginzburg–Landau equations on Riemann surfaces of higher genus

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

Research output: Contribution to journal › Article › peer-review

6 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 language	English (US)
Pages (from-to)	79-103
Number of pages	25
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	37
Issue number	1
DOIs	https://doi.org/10.1016/j.anihpc.2019.04.002
State	Published - 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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10.1016/j.anihpc.2019.04.002

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title = "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 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.",

keywords = "Elliptic equations on Riemann surfaces, Ginzburg–Landau equations, Holomorphic bundles, Superconductivity, Vortex lattices, Vortices",

author = "D. Chouchkov and Ercolani, {N. M.} and S. Rayan and Sigal, {I. M.}",

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T1 - Ginzburg–Landau equations on Riemann surfaces of higher genus

AU - Chouchkov, D.

AU - Ercolani, N. M.

AU - Rayan, S.

AU - Sigal, I. M.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - 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.

AB - 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.

KW - Elliptic equations on Riemann surfaces

KW - Ginzburg–Landau equations

KW - Holomorphic bundles

KW - Superconductivity

KW - Vortex lattices

KW - Vortices

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JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

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Ginzburg–Landau equations on Riemann surfaces of higher genus

Abstract

Keywords

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