Total mean curvature surfaces in the product space $\mathbb{S}^n\times\mathbb{R}$ and applications
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910320828612608 |
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| author | Albujer, Alma L. da Silva, Sylvia F. Santos, Fábio R. dos |
| author_facet | Albujer, Alma L. da Silva, Sylvia F. Santos, Fábio R. dos |
| contents | The total mean curvature functional for submanifolds into the Riemannian product space $\mathbb{S}^n\times\mathbb{R}$ is considered and its first variational formula is presented. Later on, two second order differential operators are defined and a nice integral inequality relating both of them is proved. Finally we prove our main result: an integral inequality for closed stationary $\mathcal{H}$-surfaces in $\mathbb{S}^n\times\mathbb{R}$, characterizing the cases where the equality is attained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04394 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Total mean curvature surfaces in the product space $\mathbb{S}^n\times\mathbb{R}$ and applications Albujer, Alma L. da Silva, Sylvia F. Santos, Fábio R. dos Differential Geometry 53C42, 53A10, 53C30 The total mean curvature functional for submanifolds into the Riemannian product space $\mathbb{S}^n\times\mathbb{R}$ is considered and its first variational formula is presented. Later on, two second order differential operators are defined and a nice integral inequality relating both of them is proved. Finally we prove our main result: an integral inequality for closed stationary $\mathcal{H}$-surfaces in $\mathbb{S}^n\times\mathbb{R}$, characterizing the cases where the equality is attained. |
| title | Total mean curvature surfaces in the product space $\mathbb{S}^n\times\mathbb{R}$ and applications |
| topic | Differential Geometry 53C42, 53A10, 53C30 |
| url | https://arxiv.org/abs/2402.04394 |