Solitons of the mean curvature flow in S2×R

Abstract

A soliton of the mean curvature flow in the product space $S^2\times R$ is a surface whose mean curvature H satisfies the equation $H=〈N,X〉$, where N is the unit normal of the surface and X is a Killing vector field of $S^2\times R$. In this paper we consider the cases that X is the vector field tangent to the second factor and the vector field associated to rotations about an axis of $S^2$, 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 rotations of $S^2$.