  In this paper we consider closed $\text{SL}(3,\mathbb{C})$-structures which
are either mean convex or tamed by a symplectic form. These notions were
introduced by Donaldson in relation to $\text{G}_2$-manifolds with boundary. In
particular, we classify nilmanifolds which carry an invariant mean convex
closed $\text{SL}(3,\mathbb{C})$-structure and those which admit an invariant
mean convex half-flat $\text{SU}(3)$-structure. We also prove that, if a
solvmanifold admits an invariant tamed closed
$\text{SL}(3,\mathbb{C})$-structure, then it also has an invariant symplectic
half-flat $\text{SU}(3)$-structure.
