Abstract
Through the application of appropriated generalized maximum principles, our aim in this work is to study Bernstein-type properties related to complete two-sided hypersurfaces immersed in a weighted warped product space. In this setting, supposing a natural comparison inequality between the weighted mean curvatures of the hypersurface and those of the slices of the slab where the hypersurface is supposed to be contained, we establish sufficient conditions which guarantee that such a hypersurface must be a slice. Furthermore, we also obtain several rigidity results concerning the slices of weighted product spaces.
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