On the classification of capillary graphs in Euclidean and non-Euclidean spaces
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914211048718336 |
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| author | Colombo, Giulio Farina, Alberto Magliaro, Marco Mari, Luciano Rigoli, Marco |
| author_facet | Colombo, Giulio Farina, Alberto Magliaro, Marco Mari, Luciano Rigoli, Marco |
| contents | We prove some rigidity and classification results for graphs with prescribed mean curvature and locally constant Dirichlet and Neumann data, for instance as they appear in capillarity problems. We consider domains in Riemannian manifolds, with emphasis on $\mathbb{R}^2$ and $\mathbb{R}^3$. We classify both the underlying domain and the resulting solution, providing general splitting theorems in this setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17813 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the classification of capillary graphs in Euclidean and non-Euclidean spaces Colombo, Giulio Farina, Alberto Magliaro, Marco Mari, Luciano Rigoli, Marco Differential Geometry Analysis of PDEs We prove some rigidity and classification results for graphs with prescribed mean curvature and locally constant Dirichlet and Neumann data, for instance as they appear in capillarity problems. We consider domains in Riemannian manifolds, with emphasis on $\mathbb{R}^2$ and $\mathbb{R}^3$. We classify both the underlying domain and the resulting solution, providing general splitting theorems in this setting. |
| title | On the classification of capillary graphs in Euclidean and non-Euclidean spaces |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2512.17813 |