Slab theorem and halfspace theorem for constant mean curvature surfaces in
Laurent Hauswirth
Université Gustave Eiffel; Université Paris-Est Créteil, Marne-la-Vallée, FranceAna Menezes
Princeton University, USAMagdalena Rodríguez
Universidad de Granada, Spain
![Slab theorem and halfspace theorem for constant mean curvature surfaces in $\mathbb H^2\times\mathbb R$ cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-rmi-volume-39-issue-1.png&w=3840&q=90)
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