Existence of Solutions to the Seiberg-Witten Vortex Equations with Exponential Decay on the Plane
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913097583689728 |
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| author | Blair, William L. Nguyen, Minh Lam |
| author_facet | Blair, William L. Nguyen, Minh Lam |
| contents | Clifford Taubes showed that the moduli space of the variational equation of the Yang-Mills-Higgs functional on the plane is non-empty, and its elements correspond to "vortices". Inspired by this result, in this paper, we show that the moduli space of the Hitchin-type dimensional reduction of the Seiberg-Witten equations on the plane contains both exponentially decayed solutions and polynomial growth solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_20043 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of Solutions to the Seiberg-Witten Vortex Equations with Exponential Decay on the Plane Blair, William L. Nguyen, Minh Lam Analysis of PDEs Mathematical Physics Complex Variables Differential Geometry 53Cxx, 57Rxx, 58Jxx, 57Kxx, 30G20, 30Cxx Clifford Taubes showed that the moduli space of the variational equation of the Yang-Mills-Higgs functional on the plane is non-empty, and its elements correspond to "vortices". Inspired by this result, in this paper, we show that the moduli space of the Hitchin-type dimensional reduction of the Seiberg-Witten equations on the plane contains both exponentially decayed solutions and polynomial growth solutions. |
| title | Existence of Solutions to the Seiberg-Witten Vortex Equations with Exponential Decay on the Plane |
| topic | Analysis of PDEs Mathematical Physics Complex Variables Differential Geometry 53Cxx, 57Rxx, 58Jxx, 57Kxx, 30G20, 30Cxx |
| url | https://arxiv.org/abs/2406.20043 |