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 , 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm8464-4-2016,
author = {Antonio W. Cunha and Eudes L. de Lima and Henrique F. de Lima and Eraldo A. Lima Jr. and Adriano A. Medeiros},
title = {Bernstein type properties of two-sided hypersurfaces immersed in a Killing warped product},
journal = {Studia Mathematica},
volume = {233},
year = {2016},
pages = {183-196},
zbl = {06586875},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8464-4-2016}
}
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) pp. 183-196. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8464-4-2016/