In this talk, we will describe the 1-parameter family of horizontal Delaunay surfaces in S2×R and H2×R with supercritical constant mean curvature. These surfaces are not equivariant but singly periodic, and they lie at bounded distance from a horizontal geodesic. We will show that horizontal unduloids are properly embedded surfaces in H2×R. We also describe the first non-trivial examples of embedded constant mean curvature tori in S2×R which are continuous deformations from a stack of tangent spheres to a horizontal invariant cylinder. They have constant mean curvature H>12. Finally, we prove that there are no properly immersed surface with critical or subcritical constant mean curvature at bounded distance from a horizontal geodesic in H2×R.
Contraseña 786875