Slab theorem and halfspace theorem for constant mean curvature surfaces in

  • Laurent Hauswirth

    Université Gustave Eiffel; Université Paris-Est Créteil, Marne-la-Vallée, France
  • Ana Menezes

    Princeton University, USA
  • Magdalena Rodríguez

    Universidad de Granada, Spain
Slab theorem and halfspace theorem for constant mean curvature surfaces in $\mathbb H^2\times\mathbb R$ cover
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Abstract

We prove that a properly embedded annular end of a surface in with constant mean curvature can not be contained in any horizontal slab. Moreover, we show that a properly embedded surface with constant mean curvature contained in and with finite topology is necessarily a graph over a simply connected domain of . For the case , the graph is entire.

Cite this article

Laurent Hauswirth, Ana Menezes, Magdalena Rodríguez, Slab theorem and halfspace theorem for constant mean curvature surfaces in . Rev. Mat. Iberoam. 39 (2023), no. 1, pp. 307–320

DOI 10.4171/RMI/1372