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.