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.

中文翻译：

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双曲空间中凸域上最小图的全局正则性

在本文中，我们研究了双曲空间中凸域上最小图方程的狄利克雷问题解的全局正则性。我们发现全局正则性仅取决于域的凸性，而与其平滑度无关。基于平移和旋转变换下问题的不变性，我们构造了该问题的超解，由此证明了该问题的最优且准确的全局正则性。