The mean curvature vector field encodes much of the extrinsic geometry of a spatial subvariety and influences the structure of the spacetime containing that subvariety. When the codimension is 2, classification of stationary spatial subvarieties in Brinkmann spacetimes. In the case of codimension 1, i.e. of spatial hypersurfaces, uniqueness results, in generalised Robertson-Walker spacetimes, of complete spatial hypersurfaces with constant mean curvature function or with controlled growth. Obtaining and solving new Calabi-Bernstein type problems.