Height estimates and topology at infinity of hypersurfaces immersed in a certain class of warped products (Q1662427)

In this paper, the authors obtain height estimates for hypersurfaces immersed in a class of warped products of the type \(\mathbb R\times_{\rho}M^n\), under the assumption that some higher-order mean curvatures are linearly related. As an application, they prove half-space theorems, which give information concerning the topology at infinity of such a hypersurface \(\Sigma^n\) when the fiber \(M^n\) is compact and \(\Sigma^n\) is noncompact, two-sided and properly immersed. Furthermore, when \(M^n\) is not necessarily compact, using a generalized version of the Omori-Yau maximum principle for trace-type differential operators, they establish new half-space theorems for these hypersurfaces.