Affiliation:
1. Università di Verona , Strada Le Grazie 15, 37134 Verona , Italy
2. 657489 Scuola Superiore Meridionale , Via Mezzocannone 4, 80138 Napoli , Italy
Abstract
Abstract
We consider a gauge-invariant Ginzburg–Landau functional
(also known as Abelian Yang–Mills–Higgs model),
on Hermitian line bundles over closed Riemannian manifolds of dimension
n
≥
3
{n\geq 3}
.
Assuming a logarithmic energy bound in the coupling parameter, we study the asymptotic behaviour of critical points
in the London limit. After a convenient choice of the gauge, we show compactness of finite-energy critical points
in Sobolev norms.
Moreover, thanks to a suitable monotonicity formula, we prove that the energy densities of critical points,
rescaled by the logarithm of the coupling parameter, converge to the weight measure of a stationary, rectifiable varifold of codimension 2.
Funder
Deutsche Forschungsgemeinschaft
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