Height estimates for constant mean curvature graphs in $\mathrm{Nil}_3$ and $\widetilde{PSL}_2(\mathbb{R})$

Abstract

In this paper we obtain height estimates for compact, constant mean curvature vertical graphs in the homogeneous spaces $\mathrm{Nil}_3$ and $\widetilde{PSL}_2(\mathbb{R})$. As a straightforward consequence, we announce a structure-type result for proper graphs defined on relatively compact domains.