Calculus of Variations and Geometric Measure Theory
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G. Canevari - Federico Luigi Dipasquale - G. Orlandi

The Yang-Mills-Higgs functional on complex line bundles: $Γ$-convergence and the London equation

created by canevari on 02 Aug 2022



Inserted: 2 aug 2022

Year: 2022

ArXiv: 2206.03327 PDF


We consider the Abelian Yang-Mills-Higgs functional, in the non-self dual scaling, on a complex line bundle over a closed Riemannian manifold of dimension $n\geq 3$. This functional is the natural generalisation of the Ginzburg-Landau model for superconductivity to the non-Euclidean setting. We prove a $\Gamma$-convergence result, in the strongly repulsive limit, on the functional rescaled by the logarithm of the coupling parameter. As a corollary, we prove that the energy of minimisers concentrates on an area-minimising surface of dimension $n-2$, while the curvature of minimisers converges to a solution of the London equation.

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