A note on the uniqueness of minimal maps into ${\mathbb{R}}^n$ via singular values

In this note, we derive a uniqueness theorem for minimal graphs of general codimension under certain restrictions closed related to the convexity (not strict convexity) of the area functional with respect to singular values, improving the result in \cite{L-O-T}. The crucial step of the proof is to show the local linearity of the singular value vectors along the geodesic homotopy of two given minimal maps.