On the upper area bound for minimal graphs in the unit ball

Abstract

A classical result establishes that the area of a minimal graph intersected with the unit ball is at most $2π$. A natural question is whether this upper bound is sharp. In this note, we resolve this by constructing a sequence of minimal graphs via solutions to a Dirichlet problem. We show that the areas of these graphs tend to $2π$, demonstrating that the bound is sharp.