We study the convexity of the area functional for the graphs of maps with respect to the singular values of their differentials. Suppose that f is a solution to the Dirichlet problem for the minimal surface system and the area functional is convex at f . Then the graph of f is stable. New criteria for the stability of minimal graphs in any co-dimension are derived in the paper by this method. Our results in particular generalize the co-dimension one case, and improve the condition in the 2003

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... per of the first author and M.-T. where p is an upper bound of the rank of df , and the condition in the 2008 paper of the first author and M.-T. Wang from det(I + (df ) T df ) ≤ 43 40 to det(I + (df ) T df ) ≤ 2.