Partial Regularity of Stable Stationary Harmonic Maps into Certain Lie Groups
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866915981104775168 |
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| author | Krantz, Jacob |
| author_facet | Krantz, Jacob |
| contents | Let $M$ be a compact Riemannian manifold, and let $G$ be a compact simple Lie group with bi-invariant metric that is not $\operatorname{Sp}(n)$ for $n \geq 8$, $E_{8}$, $F_{4}$, or $G_{2}$. We show that the singular set of any stable stationary harmonic map $u : M \to G$ has Hausdorff codimension at least four. We also find examples of maps into these manifolds with codimension four singularities to show that we cannot reduce the dimension of the singular set any further. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03809 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Partial Regularity of Stable Stationary Harmonic Maps into Certain Lie Groups Krantz, Jacob Differential Geometry Let $M$ be a compact Riemannian manifold, and let $G$ be a compact simple Lie group with bi-invariant metric that is not $\operatorname{Sp}(n)$ for $n \geq 8$, $E_{8}$, $F_{4}$, or $G_{2}$. We show that the singular set of any stable stationary harmonic map $u : M \to G$ has Hausdorff codimension at least four. We also find examples of maps into these manifolds with codimension four singularities to show that we cannot reduce the dimension of the singular set any further. |
| title | Partial Regularity of Stable Stationary Harmonic Maps into Certain Lie Groups |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2605.03809 |