On the rigidity of mean curvature flow solitons in certain semi-Riemannian warped products

Abstract

We obtain rigidity results concerning complete noncompact solitons of the mean curvature flow related to a nonsingular Killing vector field K globally defined in a semi-Riemannian space, which can be modeled as a warped product whose base corresponds to a fixed integral leaf of the distribution orthogonal to K and the warping function is equal to |K|. Our approach is based on a suitable maximum principle dealing with a notion of convergence to zero at infinity. As application, we study the uniqueness of solutions for the mean curvature flow soliton equation in these ambient spaces.