  In this paper we study the global regularity for the solution to the
Dirichlet problem of the equation of minimal graphs over a convex domain in
hyperbolic spaces.
  We find that the global regularity depends only on the convexity of the
domain but independent of its smoothness.
  Basing on the invariance of the problem under translation and rotation
transforms, we construct the super-solution to the problem, by which we prove
the optimal and accurate global regularity for this problem.
