Constant mean curvature Radial graphs over domains of $\mathbb{S}^n$
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913959020331008 |
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| author | Cruz, Flávio Cruz, José T. Oliveira, Jocel |
| author_facet | Cruz, Flávio Cruz, José T. Oliveira, Jocel |
| contents | We establish the existence of hypersurfaces with constant mean curvature and a prescribed boundary in Euclidean space, represented as radial graphs over domains of the unit sphere. Under the assumptions that the mean curvature of the domain's boundary is positive and that a subsolution exists for the associated Dirichlet problem, we extend Serrin's classical result to include the case of positive constant mean curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18496 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constant mean curvature Radial graphs over domains of $\mathbb{S}^n$ Cruz, Flávio Cruz, José T. Oliveira, Jocel Differential Geometry Analysis of PDEs 53C42, 35J60 We establish the existence of hypersurfaces with constant mean curvature and a prescribed boundary in Euclidean space, represented as radial graphs over domains of the unit sphere. Under the assumptions that the mean curvature of the domain's boundary is positive and that a subsolution exists for the associated Dirichlet problem, we extend Serrin's classical result to include the case of positive constant mean curvature. |
| title | Constant mean curvature Radial graphs over domains of $\mathbb{S}^n$ |
| topic | Differential Geometry Analysis of PDEs 53C42, 35J60 |
| url | https://arxiv.org/abs/2507.18496 |