The quantitative behavior of $α$-Yang-Mills-Higgs fields on surfaces
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908524598001664 |
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| author | Ai, Wanjun Li, Jiayu Zhu, Miaomiao |
| author_facet | Ai, Wanjun Li, Jiayu Zhu, Miaomiao |
| contents | We investigate the blow-up behavior of $α$-Yang--Mills--Higgs ($α$-YMH) fields over closed Riemannian surfaces with the target fiber $F = S^{K-1} \subset \mathbb{R}^K$ being the round sphere, focusing on the establishment of the $α$-energy identity and the no-neck property during the bubbling process. A central innovation is the identification of a hidden Jacobian structure through Hodge decomposition and a new conservation law. Furthermore, we derive a Pohozaev-type identity for $α$-YMH fields, which enables refined control of the energy density. Together, these advances ensure the validity of the $α$-energy identity as $α\to 1$. Our analysis further sharpens the Lorentz space estimates from the $L^{2,\infty}$ to the optimal $L^{2,1}$ scale, ultimately yielding the no-neck property in the blow-up regime. These results provide a unified and quantitative framework for understanding singularity formation in variational gauge theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06380 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The quantitative behavior of $α$-Yang-Mills-Higgs fields on surfaces Ai, Wanjun Li, Jiayu Zhu, Miaomiao Differential Geometry 58E15, 53C43 We investigate the blow-up behavior of $α$-Yang--Mills--Higgs ($α$-YMH) fields over closed Riemannian surfaces with the target fiber $F = S^{K-1} \subset \mathbb{R}^K$ being the round sphere, focusing on the establishment of the $α$-energy identity and the no-neck property during the bubbling process. A central innovation is the identification of a hidden Jacobian structure through Hodge decomposition and a new conservation law. Furthermore, we derive a Pohozaev-type identity for $α$-YMH fields, which enables refined control of the energy density. Together, these advances ensure the validity of the $α$-energy identity as $α\to 1$. Our analysis further sharpens the Lorentz space estimates from the $L^{2,\infty}$ to the optimal $L^{2,1}$ scale, ultimately yielding the no-neck property in the blow-up regime. These results provide a unified and quantitative framework for understanding singularity formation in variational gauge theories. |
| title | The quantitative behavior of $α$-Yang-Mills-Higgs fields on surfaces |
| topic | Differential Geometry 58E15, 53C43 |
| url | https://arxiv.org/abs/2509.06380 |