Solitons of the mean curvature flow in $\mathbb{s}^2\times\mathbb{R}$
| Autor: | López, Rafael, Munteanu, Marian Ioan |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | A soliton of the mean curvature flow in the product space $\mathbb{s}^2\times\mathbb{R}$ as a surface whose mean curvature $H$ satisfies the equation $H=\langle N,X\rangle$, where $N$ is the unit normal of the surface and $X$ is a Killing vector field. In this paper we consider the vector field tangent to the fibers and the vector field associated to a rotations about an axis of $\mathbb{s}^2$, respectively. We give a classification of the solitons with respect to these vector fields assuming that the surface is invariant under a one-parameter group of vertical translations or under a group of rotations of $\mathbb{s}^2$. Comment: 14 pages, 5 figures |
| Databáze: | arXiv |
| Externí odkaz: |
|