# Global Regularity for minimal graphs over convex domains in hyperbolic space

## TL;DR

This paper establishes that the global regularity of minimal graph solutions over convex domains in hyperbolic space depends solely on convexity, not smoothness, using super-solution construction and invariance properties.

## Contribution

It proves the optimal global regularity for minimal graphs over convex domains in hyperbolic space, independent of boundary smoothness, by constructing super-solutions based on invariance.

## Key findings

- Global regularity depends only on convexity
- Constructed super-solutions for the problem
- Achieved optimal and accurate regularity results

## Abstract

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.