Bernstein type properties of two-sided hypersurfaces immersed in a Killing warped product
Volume 233 / 2016
Studia Mathematica 233 (2016), 183-196
MSC: Primary 53C42; Secondary 53B30, 53C50.
DOI: 10.4064/sm8464-4-2016
Published online: 19 May 2016
Abstract
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 $M^n\times _\rho \mathbb R$, whose curvature of the base $M^n$ satisfies certain constraints and whose warping function $\rho $ is concave on $M^n$. For this, we study situations in which these hypersurfaces are supposed to be either parabolic, stochastically complete or, in a more general setting, $L^1$-Liouville. Rigidity results related to entire Killing graphs constructed over the base of the ambient space are also given.
