On the solution of the harmonic-divgrad PDEs system
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866929674342367232 |
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| author | Manzoni, Federico |
| author_facet | Manzoni, Federico |
| contents | We study a particular system of partial differential equations in which the harmonic, the divergence and the gradient operators of the unknown functions appear (harmonic-divgrad system). Using the Killing Hopf theorem and leveraging the properties of Riemannian manifolds with constant sectional curvature we establish the conditions under which these equations admit only the trivial solutions proving their trivialization on positive curvature space forms. The analysis of this particular system is motivated by its occurrence in the study of asymptotic symmetries in $p$-form gauge theories and in mixed symmetry tensor gauge theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07506 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the solution of the harmonic-divgrad PDEs system Manzoni, Federico Mathematical Physics High Energy Physics - Theory Analysis of PDEs We study a particular system of partial differential equations in which the harmonic, the divergence and the gradient operators of the unknown functions appear (harmonic-divgrad system). Using the Killing Hopf theorem and leveraging the properties of Riemannian manifolds with constant sectional curvature we establish the conditions under which these equations admit only the trivial solutions proving their trivialization on positive curvature space forms. The analysis of this particular system is motivated by its occurrence in the study of asymptotic symmetries in $p$-form gauge theories and in mixed symmetry tensor gauge theories. |
| title | On the solution of the harmonic-divgrad PDEs system |
| topic | Mathematical Physics High Energy Physics - Theory Analysis of PDEs |
| url | https://arxiv.org/abs/2501.07506 |