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Complete Foliations of Space Forms by Hypersurfaces
A. Caminha, P. Sousa, F. Camargo
We study foliations of space forms by complete hypersurfaces, under some mild conditions on its higher order mean curvatures. In particular, in Euclidean space we obtain a Bernstei…
A Generalized Maximum Principle for Yau's Square Operator, with Applications to the Steady State Space
Antonio Caminha, Henrique de Lima
We derive, for the square operator of Yau, an analogue of the Omori-Yau maximum principle for the Laplacian. We then apply it to obtain nonexistence results concerning complete spa…
Complete Vertical Graphs with Constant Mean Curvature in Semi-Riemannian Warped Products
Antonio Caminha, Henrique F. de Lima
We obtain necessary conditions for the existence of complete vertical graphs of constant mean curvature in the Hyperbolic and Steady State spaces. In the two-dimensional case we pr…
Stability of Spacelike Hypersurfaces in Foliated Spacetimes
A. Barros, A. Brasil, A. Caminha
We show that a given closed spacelike hypersurface with constant mean curvature and warping function satisfying ϕ''\geq \ma\{Hϕ'',0\…