Weakly trapped submanifolds immersed in generalized Robertson-Walker spacetimes

We deal with codimension two weakly trapped submanifolds (that is, the mean curvature vector field is causal) immersed in a generalized Robertson-Walker (GRW) spacetime. Under suitable hypothesis, we are able to prove that such a spacelike submanifold is immersed into a slice of the ambient space. For this, we use three main core concepts: the well known generalized maximum principle of Omori and Yau, stochastic completeness and another appropriate maximum principle at infinity due to Yau. We also construct a nontrivial example of weakly trapped submanifold in the static GRW spacetime −R×H2×R, illustrating the importance of our results.