Uniqueness of constant mean curvature surfaces properly immersed in a slab

• Autores: Luis José Alías Linares , Marcos Dajczer
• Localización: Commentarii mathematici helvetici, ISSN 0010-2571, Vol. 81, Nº 3, 2006, págs. 653-663
• Idioma: inglés
• DOI: 10.4171/cmh/68
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• Resumen

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