Rigidity of Solitons to the Mean Curvature Flow in ${\mathbb{H}}^3$ as Translation Surfaces

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 $\alpha$ and $\beta$ 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.