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Uniqueness of constant mean curvature surfaces properly immersed in a slab. (English) Zbl 1110.53039
The authors study complete immersed surfaces contained in a slab of a warped product × ρ 2 , where 2 is complete with nonnegative Gaussian curvature. Under certain restrictions on the mean curvature of the surface, the authors prove that such an immersion does not exist or must be a leaf of the trivial totally umbilical foliation t{t}× 2 .

MSC:
53C42Immersions (differential geometry)
53A10Minimal surfaces, surfaces with prescribed mean curvature