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arXiv · 2511.21349

Multiplicity of solutions for Gross-Pitaevskii equations on Riemannian manifolds

Dario Corona·Stefano Nardulli·Ramon Oliver-Bonafoux·Giandomenico Orlandi
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Abstract

We provide a multiplicity result for solutions of time-independent Gross-Pitaevskii equations on closed Riemannian manifolds. Such solutions arise as (possibly non-minimizing) critical points of the Ginzburg-Landau energy having prescribed momentum according to a given tangent velocity field. Lower bounds on the multiplicity of solutions are obtained in terms of the topology of the maximum velocity set, in the small momentum and vorticity core size regime. The proof relies on methods from critical point theory and $Γ$-convergence for Ginzburg-Landau functionals as well as on some new results for codimension 2 isoperimetric-type problems in the small flux regime, possibly of independent interest.

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Dario Corona, Stefano Nardulli, Ramon Oliver-Bonafoux, Giandomenico Orlandi. 2025-11-26. Multiplicity of solutions for Gross-Pitaevskii equations on Riemannian manifolds. https://arxiv.org/abs/2511.21349

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