Half-space type theorems in warped product spaces with one-dimensional factor

Abstract

This work states some half-space type theorems in a warped product space of the form I ×ρM, where \({I \subseteq {\bf R}}\) is an open interval and M is either a compact n-manifold, or a complete simply connected surface with constant curvature c ≤ 0. Such theorems generalize the classical half-space theorem for minimal surfaces in R3, obtained by Hoffmann and Meeks (Invent Math 101:373–377, 1990), and recent results for surfaces contained in a slab of R ×ρM, obtained by Dajczer and Alias (Comment Math Helvetici 81:653–663, 2006).