The class of grim reapers in $\mathbb{H}^2\times\mathbb{R}$
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910332060958720 |
|---|---|
| author | Bueno, Antonio López, Rafael |
| author_facet | Bueno, Antonio López, Rafael |
| contents | We study translators of the mean curvature flow in the product space $\h^2\times\r$. In $\h^2\times\r$ there are three types of translations: vertical translations due to the factor $\r$ and parabolic and hyperbolic translations from $\h^2$. A grim reaper in $\h^2\times\r$ is a translator invariant by a one-parameter group of translations. The variety of translators and translations in $\h^2\times\r$ makes that the family of grim reapers particularly rich. In this paper we give a full classification of the grim reapers of $\h^2\times\r$ with a description of their geometric properties. In some cases, we obtain explicit parametrizations of the surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05772 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The class of grim reapers in $\mathbb{H}^2\times\mathbb{R}$ Bueno, Antonio López, Rafael Differential Geometry Primary 53A10, Secondary 53C44, 53C21, 53C42 We study translators of the mean curvature flow in the product space $\h^2\times\r$. In $\h^2\times\r$ there are three types of translations: vertical translations due to the factor $\r$ and parabolic and hyperbolic translations from $\h^2$. A grim reaper in $\h^2\times\r$ is a translator invariant by a one-parameter group of translations. The variety of translators and translations in $\h^2\times\r$ makes that the family of grim reapers particularly rich. In this paper we give a full classification of the grim reapers of $\h^2\times\r$ with a description of their geometric properties. In some cases, we obtain explicit parametrizations of the surfaces. |
| title | The class of grim reapers in $\mathbb{H}^2\times\mathbb{R}$ |
| topic | Differential Geometry Primary 53A10, Secondary 53C44, 53C21, 53C42 |
| url | https://arxiv.org/abs/2402.05772 |