Minimal Graphs in the Hyperbolic Space with Singular Asymptotic   Boundaries
  We study asymptotic behaviors of solutions $f$ to the Dirichlet problem for minimal graphs in the hyperbolic space with singular asymptotic boundaries under the assumption that the boundaries are piecewise regular with positive curvatures. We derive an estimate of such solutions by the corresponding solutions in the intersections of interior tangent balls. The positivity of curvatures plays an important role. 
Qing Han, Weiming Shen, Yue Wang
math.AP