Bernstein type properties of two-sided hypersurfaces immersed in a Killing warped product
Studia Mathematica, Tome 233 (2016) no. 2, p. 183.

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Our purpose is to apply suitable maximum principles in order to obtain Bernstein type properties for two-sided hypersurfaces immersed with constant mean curvature in a Killing warped product M ⁿ × ρ ℝ , whose curvature of the base Mⁿ satisfies certain constraints and whose warping function ρ is concave on Mⁿ. For this, we study situations in which these hypersurfaces are supposed to be either parabolic, stochastically complete or, in a more general setting, L¹-Liouville. Rigidity results related to entire Killing graphs constructed over the base of the ambient space are also given.
Classification : 53C42, 53C50, 53B30
Mots-clés : Killing warped product, parabolic hypersurfaces, stochastically complete hypersurfaces, L1-Liouville hypersurfaces, entire Killing graphs 
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     title = {Bernstein type properties of two-sided hypersurfaces immersed in a {Killing} warped product},
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Antonio W. Cunha; Eudes L. de Lima; Henrique F. de Lima; Eraldo A. Lima Jr.; Adriano A. Medeiros. Bernstein type properties of two-sided hypersurfaces immersed in a Killing warped product. Studia Mathematica, Tome 233 (2016) no. 2, p. 183. https://geodesic-test.mathdoc.fr/item/STUMA_2016__233_2_285827/