Abstract: Firstly, by applying the corresponding infinitesimal generators of Heisenberg group on the factorable surfaces, we obtained four kinds of one-parameter surface families. Secondly, by using the analytical method, we established the mean curvature flow (MCF) equations of three nontrivial surface families, and obtained the conclusion that the existence time of the MCF and the soliton solution of the minimal MCF of two kinds of the surface families were saddle surfaces.

Key words:  , Heisenberg group, mean curvature flow (MCF), Lie algebra, factorable surface, soliton solution