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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2507.12865 |
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Table des matières:
- Consider the energy $E_α[Σ]=\int_Σ|p|^α\, dΣ$, where $Σ$ is a surface in Euclidean space $\r^3$ and $α\in\r$. We prove that planes and spheres are the only stationary surfaces for $E_α$ with constant Gauss curvature. We also characterize these surfaces assuming that a principal curvature is constant or that the mean curvature is constant.