Rigidity of Solitons to the Mean Curvature Flow in $\mathbb{H}^3$ as Translation Surfaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911288457691136 |
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| author | Ferreira, Tarcios Andrey Santos, João Paulo dos |
| author_facet | Ferreira, Tarcios Andrey Santos, João Paulo dos |
| contents | In the half-space model of the hyperbolic three space with the hyperbolic metric, this same space can be seen as the Lie group, hence, a translation surface is a surface that is given by the product of two curves $α$ and $β$ in this group. Here we present the rigidity of this kind of surfaces for some particular products in the context of minimal surfaces and solitons to the Mean Curvature Flow, also known as self-similar solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21545 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigidity of Solitons to the Mean Curvature Flow in $\mathbb{H}^3$ as Translation Surfaces Ferreira, Tarcios Andrey Santos, João Paulo dos Differential Geometry 53C40 53C42 53E10 In the half-space model of the hyperbolic three space with the hyperbolic metric, this same space can be seen as the Lie group, hence, a translation surface is a surface that is given by the product of two curves $α$ and $β$ in this group. Here we present the rigidity of this kind of surfaces for some particular products in the context of minimal surfaces and solitons to the Mean Curvature Flow, also known as self-similar solutions. |
| title | Rigidity of Solitons to the Mean Curvature Flow in $\mathbb{H}^3$ as Translation Surfaces |
| topic | Differential Geometry 53C40 53C42 53E10 |
| url | https://arxiv.org/abs/2511.21545 |