, Volume 24, Issue 2, pp 1126-1143
Date: 12 Oct 2012

On the Unicity of Complete Hypersurfaces Immersed in a Semi-Riemannian Warped Product

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Our purpose is to apply appropriate generalized maximum principles in order to study the unicity of complete hypersurfaces immersed in a semi-Riemannian warped product, which is supposed to obey a suitable convergence condition. In this setting, by assuming a natural comparison inequality between the r-th mean curvatures of the hypersurface and the ones of the slices of the slab where the hypersurface is contained, we establish sufficient conditions to guarantee that such a hypersurface must be a slice.