A new family of translating solitons in hyperbolic space
| Autor: | Bueno, Antonio, López, Rafael |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | If $\xi$ is a Killing vector field of the hyperbolic space $\h^3$ whose flow are parabolic isometries, a surface $\Sigma\subset\h^3$ is a $\xi$-translator if its mean curvature $H$ satisfies $H=\langle N,\xi\rangle$, where $N$ is the unit normal of $\Sigma$. We classify all $\xi$-translators invariant by a one-parameter group of rotations of $\h^3$, exhibiting the existence of a new family of grim reapers. We use these grim reapers to prove the non-existence of closed $\xi$-translators. Comment: 11 pages, 2 figures |
| Databáze: | arXiv |
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