Hyperbolic Willmore surfaces of revolution: Half-Space model

Hyperbolic analogues of surfaces of revolution, in ${\mathbb H}^3$, namely surfaces invariant under an action of $SO(1,1)$ on ${\mathbb H}^3$. The images shown are projections to the half-space model for ${\mathbb H}^3$. The plane $z=0$ corresponds to the boundary at infinity. These surfaces in general correspond to several surfaces in the two copies of ${\mathbb H}^3$ (above and below the plane), that meet smoothly at the boundary.         Read about this work...