Complete space-like self-expanders in the Minkowski space

We study complete space-like self-expanders in the Minkowski space. By using a maximum principle of Omori–Yau type, we obtain rigidity theorems on n-dimensional complete space-like self-expanders in the Minkowski space Rn+11. For dimensions 2 and 3, we also classify them under the assumption of constant squared norm of the second fundamental form.