We prove an Alexandrov-type theorem for a quotient space of ℍ2×ℝ. More precisely, we classify the compact embedded surfaces with constant mean curvature in the quotient of ℍ2×R by a subgroup of isometries generated by a horizontal translation along horocycles of ℍ2 and a vertical translation. We also construct some examples of periodic minimal surfaces in ℍ2×ℝ and we prove a multivalued Rado theorem for small perturbations of the helicoid in ℍ2×ℝ.
All Science Journal Classification (ASJC) codes
- Alexandrov reflection
- Constant mean curvature surface
- Periodic surface