Optimal regularity of minimal graphs in the hyperbolic space

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 Ω⊂Rn$$\Omega \subset \mathbb R^n$$ has a nonnegative mean curvature and prove an optimal regularity f∈C1n+1(Ω¯)$$f\in C^{\frac{1}{n+1}}(\bar{\Omega })$$. We can improve the Hölder exponent for f if certain combinations of principal curvatures of the boundary do not vanish, a phenomenon observed by F.-H. Lin.