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.
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