New characterizations of totally geodesic hypersurfaces in anti-de Sitter space H1n+1

By extending Yau’s technique, we obtain rigidity results to complete maximal spacelike hypersurfaces in anti-de Sitter space, imposing suitable conditions on both the norm of the second fundamental form and a certain height function naturally attached to the hypersurface. We also characterize complete maximal spacelike graphs satisfying a certain assumption on the gradient of the function which determines the graph.