CMC Graphs With Planar Boundary in ${\mathbb{H}}^2\times \mathbb{R}$

Ari J. Aiolfi, Patrícia Klaser

It is known that for $\Omega \subset {\mathbb{R}}^2$ an unbounded convex domain and $H>0$, there exists a graph $G\subset {\mathbb{R}}^3$ of constant mean curvature $H$ over $\Omega$ with $\p…