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Title: Characterizations of minimal hypersurfaces immersed in certain warped products
Authors: Lima, Eudes L. de
Lima, Henrique F. de
Lima, Eraldo A.
Medeiros, Adriano A.
Keywords: Killing warped product;Constant mean curvature hypersurfaces;Minimal hypersurfaces;Totally geodesic hypersurfaces;Hipersuperficies de curvatura media constante;Hipersuperficies mínimas;Hipersuperficies totalmente geodésicas
Issue Date: 2019
Publisher: Universidad de Extremadura
Abstract: Our purpose in this paper is to investigate when a complete two-sided hypersurface immersed with constant mean curvature in a Killing warped product Mⁿ X ⍴ℝ, whose Riemannian base Mⁿ has sectional curvature bounded from below and such that the warping function ⍴ ∈ C∞(M) is supposed to be concave, is minimal (and, in particular, totally geodesic) in the ambient space. Our approach is based on the application of the well known generalized maximum principle of Omori-Yau.
DOI: 10.17398/2605-5686.34.1.123
Appears in Collections:Extracta Mathematicae Vol. 34, nº 1 (2019)

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