Refined Asymptotics for Minimal Graphs in the 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 $f.$