Abstract
In this paper, we obtain new parametric uniqueness results for complete constant weighted mean curvature hypersurfaces under suitable geometric assumptions in weighted warped products. Furthermore, we also prove very general Bernstein type results for the constant mean curvature equation for entire graphs in these ambient spaces.
Highlights
In the last decades, constant mean curvature hypersurfaces in Riemannian manifolds have been deeply studied. is is because that such hypersurfaces exhibit nice Bernstein type properties
Let Mn be a connected n( ≥ 2)-dimensional oriented Riemannian manifold and I ⊂ R be an open interval endowed with the metric dt2
In order to prove our uniqueness results in weighted warped product Mn+1, we need a few previous results
Summary
Constant mean curvature hypersurfaces in Riemannian manifolds have been deeply studied. is is because that such hypersurfaces exhibit nice Bernstein type properties. The weighted manifold Mf associated with a complete Riemannian manifold (M, g) and a smooth positive function f on M is the triple (M, g, dμ e− fdM), where dM is the volume element of M In this setting, we will consider the Bakry–Emery–Ricci tensor (see [7]) which is a generalization of the standard. Salamanca and Salavessa [9] obtained uniqueness results for complete weighted minimal hypersurfaces (that is, those whose weighted mean curvature identically vanishes) in a weighted warped product whose fiber is a parabolic manifold. Our aim in this paper is to obtain new Bernstein type results for complete constant weighted mean curvature hypersurfaces in weighted warped products.
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