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June 2021 Existence and limiting behavior of min-max solutions of the Ginzburg–Landau equations on compact manifolds
Daniel Stern
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J. Differential Geom. 118(2): 335-371 (June 2021). DOI: 10.4310/jdg/1622743143

Abstract

We use a natural two-parameter min-max construction to produce critical points of the Ginzburg–Landau functionals on a compact Riemannian manifold of dimension $\geq 2$. We investigate the limiting behavior of these critical points as $\varepsilon \to 0$, and show in particular that some of the energy concentrates on a nontrivial stationary, rectifiable $(n-2)$-varifold as $\varepsilon \to 0$, suggesting connections to the min-max construction of minimal $(n-2)$-submanifolds.

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Daniel Stern. "Existence and limiting behavior of min-max solutions of the Ginzburg–Landau equations on compact manifolds." J. Differential Geom. 118 (2) 335 - 371, June 2021. https://doi.org/10.4310/jdg/1622743143

Information

Received: 11 July 2017; Published: June 2021
First available in Project Euclid: 3 June 2021

Digital Object Identifier: 10.4310/jdg/1622743143

Rights: Copyright © 2021 Lehigh University

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Vol.118 • No. 2 • June 2021
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