= Minimal graphical cone is a plane
If a smooth <minimal surface equation for a graph> solution on $\mathbb R^n\setminus\{0\}$ is homogeneous of degree one, with $n\geq2$, then its graph extends to a plane through zero. Its <gradient> is homogeneous of degree zero, so $|Du|^2$ attains a global maximum on the unit sphere. The <strong maximum principle for elliptic operators> makes it constant. The differentiated equation in the <gradient maximum principle for a minimal graph> then forces $D^2u=0$, and degree-one homogeneity removes the affine constant. This argument applies to cones that are graphs of smooth functions away from their vertex; it is not a claim that every <minimal surface> cone is flat.
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