Asymptotics of Minimizers for Ginzburg--Landau-type Functionals in High Dimensions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866913093828739072 |
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| author | Canevari, Giacomo Fu, Haotong Wang, Wei |
| author_facet | Canevari, Giacomo Fu, Haotong Wang, Wei |
| contents | We investigate local minimizers of Ginzburg--Landau-type functionals in dimension $n\geq 3$ that satisfy logarithmic energy bounds, assuming the potential has a vacuum manifold with a finite fundamental group. We show that the normalized energy measures converge to an $(n-2)$-rectifiable measure associated with a stationary varifold, with quantized density determined by the homotopy classes of the vacuum manifold. Away from the support of the $(n-2)$-rectifiable measure, the minimizers converge strongly in $H^1_{\text{loc}}$ to a minimizing harmonic map, which is smooth outside an $(n-3)$-rectifiable singular set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04442 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotics of Minimizers for Ginzburg--Landau-type Functionals in High Dimensions Canevari, Giacomo Fu, Haotong Wang, Wei Analysis of PDEs Differential Geometry We investigate local minimizers of Ginzburg--Landau-type functionals in dimension $n\geq 3$ that satisfy logarithmic energy bounds, assuming the potential has a vacuum manifold with a finite fundamental group. We show that the normalized energy measures converge to an $(n-2)$-rectifiable measure associated with a stationary varifold, with quantized density determined by the homotopy classes of the vacuum manifold. Away from the support of the $(n-2)$-rectifiable measure, the minimizers converge strongly in $H^1_{\text{loc}}$ to a minimizing harmonic map, which is smooth outside an $(n-3)$-rectifiable singular set. |
| title | Asymptotics of Minimizers for Ginzburg--Landau-type Functionals in High Dimensions |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2605.04442 |