H.F. de Lima

Bernstein-type theorems in semi-Riemannian warped products

This paper deals with complete hypersurfaces immersed in the (n + 1)-dimensional hyperbolic and steady state spaces. By applying a technique of S. T. Yau and imposing suitable conditions on both the r-th mean curvatures and on the norm of the gradient of the height function, we obtain Bernstein-type results in each of these ambient spaces.

On the r-stability of spacelike hypersurfaces

Abstract In this paper we study the strong stability of spacelike hypersurfaces with constant r -th mean curvature in Robertson–Walker spacetimes. In particular, we treat the case in which the ambient spacetime is the de Sitter space.