# Refined Asymptotics for Minimal Graphs in the Hyperbolic Space

## TL;DR

This paper investigates the boundary behavior of solutions to the minimal graph Dirichlet problem in hyperbolic space, especially near singular boundary points, providing refined asymptotic estimates for the case when n=2.

## Contribution

It characterizes boundary behaviors at singular points and offers refined asymptotic estimates for solutions in hyperbolic space, advancing understanding of minimal graphs with complex boundary conditions.

## Key findings

- Boundary behavior characterized at singular points
- Refined estimates obtained for n=2 case
- Enhanced understanding of minimal graphs in hyperbolic space

## Abstract

We study the boundary behaviors of solutions $f$ to the Dirichlet problem for minimal graphs in the hyperbolic space with singular asymptotic boundaries and characterize the boundary behaviors of $f$ at the points strictly located in the tangent cones at the singular points on the boundary. For $n=2$, we also obtain a refined estimate of $f.$