A Note on the Stability and Uniqueness for Solutions to the Minimal Surface System

In this note, we show that the solution to the Dirichlet problem for the minimal surface system is unique in the space of distance-decreasing maps. This follows as a corollary of the following stability theorem: if a minimal submanifold is the graph of a (strictly) distance-decreasing map, then is (strictly) stable. We also give another criterion for the stability which covers the codimension one case. All theorems are proved in a more general setting, which concerns minimal maps between Riemannian manifolds. The complete statements of the results appear in Theorem 3.1, Theorem 3.2, and Theorem 4.1