Structural Equations for Critical Points of Conformally Invariant Curvature Energies in 4d
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908600382783488 |
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| author | Bernard, Yann |
| author_facet | Bernard, Yann |
| contents | This paper considers the Euler-Lagrange equations satisfied by the critical points of a large class of conformally invariant extrinsic energies for 4-manifolds immersed into Euclidean space (any codimension). Using invariances and Noether's theorem, we convert the Euler-Lagrange equation in a system of equations with analytically favourable structures. The present paper generalises to the four-dimensional setting ideas originally developed by Tristan Rivière in his study of the Willmore energy in two dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01179 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structural Equations for Critical Points of Conformally Invariant Curvature Energies in 4d Bernard, Yann Differential Geometry 35G50, 53B20, 53B25, 53C42, 53C21 This paper considers the Euler-Lagrange equations satisfied by the critical points of a large class of conformally invariant extrinsic energies for 4-manifolds immersed into Euclidean space (any codimension). Using invariances and Noether's theorem, we convert the Euler-Lagrange equation in a system of equations with analytically favourable structures. The present paper generalises to the four-dimensional setting ideas originally developed by Tristan Rivière in his study of the Willmore energy in two dimensions. |
| title | Structural Equations for Critical Points of Conformally Invariant Curvature Energies in 4d |
| topic | Differential Geometry 35G50, 53B20, 53B25, 53C42, 53C21 |
| url | https://arxiv.org/abs/2509.01179 |