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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 $\mathbb{R}\times_\rho {\mathbb{P}}^2$, where $\mathbb{P}^2$ 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 $t\in {\mathbb{R}}\to \{t\}\times {\mathbb{P}}^2$.

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