Removable Singularities of Solutions of the Minimal Surface Equation

Suppose that $G$ is a bounded domain in $\mathbb{R}^n$ ($n\ge 2$), $E\ne G$ is a relatively closed set in $G$, and $0<\alpha<1$. We prove that $E$ is removable for solutions of the minimal surface equation in the class $C^{1,\alpha}(G)_{\operatorname{loc}}$ if and only if the ($n-1+\alpha$)-dimensional Hausdorff measure of $E$ is zero.