In this note, we show that the solution to the Dirichlet problem for theminimal surface system in any codimension is unique in the space ofdistance-decreasing maps. This follows as a corollary of the followingstability theorem: if a minimal submanifold $\Sigma$ is the graph of a(strictly) distance-decreasing map, then $\Sigma$ is (strictly) stable. It isknown that a minimal graph of codimension one is stable without assuming thedistance-decreasing condition. We give another criterion for the stability interms of the two-Jacobians of the map which in particular covers thecodimension one case. All theorems are proved in the more general setting forminimal maps between Riemannian manifolds.
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