Compact embedded surfaces with constant mean curvature in ${\mathbb{S}}^2\times \mathbb{R}$

José M. Manzano, Francisco Torralbo

We obtain compact orientable embedded surfaces with constant mean curvature $0<H<\frac{1}{2}$ and arbitrary genus in ${\mathbb{S}}^2\times \mathbb{R}$. These surfaces have dihedral sy…