We prove that a properly embedded annular end of a surface in H2 X R with constant mean curvature 0 < H ≤ 1=2 can not be contained in any horizontal slab. Moreover, we show that a properly embedded surface with constant mean curvature 0 < H ≤ 1=2 contained in H2 X Œ0; C1/ and with finite topology is necessarily a graph over a simply connected domain of H2. For the case H D 1=2, the graph is entire.
All Science Journal Classification (ASJC) codes
- Constant mean curvature surface
- halfspace theorem
- slab theorem