Preprint A369/2005
Uniqueness of constant mean curvature surfaces properly immersed in a slab

Marcos Dajczer | Alias, Luis

**Keywords: **

We study complete properly immersed surfaces contained in a slab of a warped product $\R\times_\varrho\Pes^2$, where $\Pes^2$ 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 $t\in\R\mapsto\{t\}\times\Pes^2$.