  We prove that a strictly stable minimal $C^2_h$ intrinsic graph G is locally
area-minimizing, i.e. given any $C^1_h$ graph $S$ with the same boundary,
$\text{Area}(G)<\text{Area}(S)$ unless $G=S$. As a consequence we show the
existence and the uniqueness of $C^\infty$ minimal graphs with prescribed small
boundary datum.
