JournalscmhVol. 81 , No. 3DOI 10.4171/cmh/68

Uniqueness of constant mean curvature surfaces properly immersed in a slab

  • Luis J. Alías

    Universidad de Murcia, Spain
  • Marcos Dajczer

    Instituto de Matemática Pura e Aplicada , Rio De Janeiro, Brazil
Uniqueness of constant mean curvature surfaces properly immersed in a slab cover

Abstract

We study complete properly immersed surfaces contained in a slab of a warped product R×ϱP2\mathbb{R}\times_\varrho\mathbb{P}^2, where P2\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 tR{t}×P2t \in \mathbb{R}\mapsto \{t\} \times \mathbb{P}^2.