We study complete properly immersed surfaces contained in a slab of a warped product , where is complete with nonnegative Gaussian curvature. Under certain restrictions on the mean curvature of the surface we show that such an immersion does not exists or must be a leaf of the trivial totally umbilical foliation .
Cite this article
Luis J. Alías, Marcos Dajczer, Uniqueness of constant mean curvature surfaces properly immersed in a slab. Comment. Math. Helv. 81 (2006), no. 3, pp. 653–663DOI 10.4171/CMH/68