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arXiv · 1704.03422

Ginzburg-Landau equations on Riemann surfaces of higher genus

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

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D. Chouchkov, N. M. Ercolani, S. Rayan, I. M. Sigal. 2017-04-11. Ginzburg-Landau equations on Riemann surfaces of higher genus. https://doi.org/10.1016/j.anihpc.2019.04.002

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