Optimal regularity of minimal graphs in the hyperbolic space

Abstract

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 Holder exponent for f if certain combinations of principal curvatures of the boundary do not vanish, a phenomenon observed by F.-H. Lin.