Ginzburg-Landau equations on non-compact Riemann surfaces

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We study the Ginzburg-Landau equations on line bundles over non-compact Riemann surfaces with constant negative curvature. We prove existence of solutions with energy strictly less than that of the constant curvature (magnetic field) one. These solutions are the non-commutative generalizations of the Abrikosov vortex lattice of superconductivity. Conjecturally, they are (local) minimizers of the Ginzburg-Landau energy. We obtain precise asymptotic expansions of these solutions and their energies in terms of the curvature of the underlying Riemann surface. Among other things, our result shows the spontaneous breaking of the gauge-translational symmetry of the Ginzburg-Landau equations.

TidsskriftJournal of Functional Analysis
Udgave nummer8
Antal sider52
StatusUdgivet - 2023

Bibliografisk note

Funding Information:
J. Zhang is supported by Danish National Research Foundation grant CPH-GEOTOP-DNRF151 , The Niels Bohr Grant of The Royal Danish Academy of Sciences and Letters , and NSERC Grant No. NA7901 . The research of IMS is supported in part by NSERC Grant No. NA7901 .

Publisher Copyright:
© 2023 The Author(s)

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