  We discuss the global regularity of solutions $f$ to the Dirichlet problem
for minimal graphs in the hyperbolic space when the boundary of the domain
$\Omega\subset\mathbb R^n$ has a nonnegative mean curvature and prove an
optimal regularity $f\in C^{\frac{1}{n+1}}(\bar{\Omega})$. We can improve the
H\"older exponent for $f$ if certain combinations of principal curvatures of
the boundary do not vanish, a phenomenon observed by F.-H. Lin.
