Axisymmetric stationary surfaces for the moment of inertia
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915727086190592 |
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| author | Dierkes, Ulrich López, Rafael |
| author_facet | Dierkes, Ulrich López, Rafael |
| contents | We investigate axisymmetric surfaces in Euclidean space that are stationary for the energy $E_α=\int_Σ|p|^α\, dΣ$. By using a phase plane analysis, we classify these surfaces when they intersect orthogonally the rotation axis. We also give some applications of the maximum principle characterizing the closed stationary surfaces and the compact stationary surfaces with boundary a circle when $α=-2$. Finally, we prove that helicoidal stationary surfaces must be rotational surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12392 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Axisymmetric stationary surfaces for the moment of inertia Dierkes, Ulrich López, Rafael Differential Geometry 53A10, Secondary: 53C42 We investigate axisymmetric surfaces in Euclidean space that are stationary for the energy $E_α=\int_Σ|p|^α\, dΣ$. By using a phase plane analysis, we classify these surfaces when they intersect orthogonally the rotation axis. We also give some applications of the maximum principle characterizing the closed stationary surfaces and the compact stationary surfaces with boundary a circle when $α=-2$. Finally, we prove that helicoidal stationary surfaces must be rotational surfaces. |
| title | Axisymmetric stationary surfaces for the moment of inertia |
| topic | Differential Geometry 53A10, Secondary: 53C42 |
| url | https://arxiv.org/abs/2507.12392 |